# Bearings Maths Trigonometry

Khan Academy Trigonometry Video Iintroduction, Example, Another Example. Find PowerPoint Presentations and Slides using the power of XPowerPoint. In Chapter 5 students are asked to use the free open-source software Gnuplot to graph some functions. us/BySubject/Trigonometry/Trigonometry_Semester. In this case, finding the right basic trigonometric functions to relate the angles and measurements are crucial for setting up and solving the problem correctly. Please click the picture to the right to find out more about retired greyhounds. This comprehensive maths assessment can be used at the end of a scheme of work on 2D trigonometry in right-angled triangles. Converting from bearing to degrees is a straightforward process when you know the basics. We’ve all been there. uk for - Lessons and worksheets suitable for the 9 - 1 GCSE Specification - A-Level teaching resources for Core 1, Core 2, Core 3, Core 4, Decision 1 and Statistics 1 - Teaching resources for Level 3 Core Mathematics - Schemes of work for Higher and Foundation GCSE. 1-2 minutes). The bearing of B from A is 075 degrees. US http://www. com; Find the Treasure - MathsPad. What are Bearings in Maths? A bearing measures the movement of an angle in a clockwise direction and always on the north line. Practice 1. twelve minutes later it bears 67 deg east of south. The bearing to a point is the angle measured in a clockwise direction from the north line. When labeling the sides and angles of the triangle ABC, the convention is that each side is labeled with same letter as the opposite angle. 2 Page 6 of 109 June 12, 2018. Bearings Challenges 03. Area of a non-right angle triangle (3 side lengths) (CAS) Basic trigonometry Powered by Create your own unique website with customizable templates. Receive All Updated And New Maths Lessons By E-mail Enter your e-mail address below and be the first to receive all new and updated lessons and resources. Mixed Trigonometry Questions. Bearings work by giving you a set number of degrees to turn clockwise from North. Do you teach the topic again, bearing in mind that 80% of your class gained 100% in the homework?. Non-calculator trigonometry (Problem solving 1) 853. Question)2:) Write)down)the)bearing)of)the)boat)fromthe)lighthouse)in)each)of)the)following. It is the longest side of the triangle. The angle of depression of the boat is. One complete revolution as shown below is 360, and parts of a revolution are measured proportionately. School students can use the free math lessons to help understand their school homework and prepare for exams and assignments. This is a text on elementary trigonometry, designed for students who have completed courses in high-school … These are homework exercises to accompany Corral's "Elementary Trigonometry" Textmap. Find x and H in the right triangle below. This is always opposite to the right angle. understand the properties and relationship among geometrical objects;. PLEASE NOTE: This navigation system is still under development. How To Learn Trigonometry Intuitively. I needed to work out. Math Posters - Pythagoras, Trigonometry x2, Angle Rules and Bearings (5 Posters) These are 5 Fantastic Math Posters that accompany my whole lessons and 'colour me in sheets' (doodle notes). A train travels on a bearing of ! 25° ! until it is 285km south of its starting point. A collection of videos, activities and worksheets that are suitable for A Level Maths. Most bearing word problems involving trigonometry and angles can be reduced to finding relationships between angles and the measurements of the sides of a triangle. The exterior angle to the triangle is therefore 180 - 35 = 145 degrees. This is the relative bearing of the first hiker from the viewpoint of the second hiker. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Ready-to-use mathematics resources for Key Stage 3, Key Stage 4 and GCSE maths classes. on numerous topics. Bearing of B from C. Math You Need > Trigonometry > Trigonometry Practice Problems Trigonometry practice problems Try solving these as much as you can on your own, and if you need help, look at the hidden solutions. The area of triangle is 38 square. Edit: Was kindly answered, thank you. The exercises for this page are a bit different to the majority of the exercises in this trigonometry book. How far west has it travelled? 2. to find missing angles and sides if you know any 3 of the sides or angles. Learn what Bearings are and how to solve questions involving Bearings and pass your math exams! You will understand how Trigonometry will help you to solve questions with Bearings looking at free maths videos and example questions. Reference : Maths for HK4B P. You must be a member in order to access this content. Thus here we have discussed Trigonometry and its importance as every student of math is expected to know about the application of this branch of mathematics in daily life. This eBook introduces the related subjects of Pythagoras' theorem, trigonometry and similarity, as Pythagoras' theorem relates to all right-angles triangles, trigonometry as it relates to angles and ratios of sine, cosine and tangent in right-angl. Kelly Oakes BuzzFeed Staff, UK. back to top. They will first. For an illustration of these basic trigonometry concepts with further explanations, please click here. Find the distance between the target and the gun nearer to it. 1) Choose a point on the map, and write down its location (don't mark anything on the map). It will consist of the following four sessions: IQM: Modelling and estimation chapter 4 and Answers. Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here. In university maths it is much more common to give angles in radians rather than degrees. Bearings are angles in degrees, which are measured clockwise from North. Due west means directly west (on a bearing of 270°) Let's refer to the intersection of the NS and EW line #C# - the middle of the compass,. 13º - 45º (angles round a point) = 262º (to the nearest whole number). Buoy 1 was used as the starting line. Practical use of Trigonometry. Solution for Р3 (x, у)3у35х-4. HOMEWORK FOR BEARING CALCULATION AND TRIGONOMETRY N85°E 100B Bearing and Distance from A to B, B to C, C to D , D to A are showed above Find: ZBAD, ZCBA, ZDCB, ZADC CALCULATE THE DISTANCE OF AC, DB, VALUE OF ZDBA, ZBDC. For example, the bearing of A from B is 065º. There are two systems used for describing bearings: True Bearings – measured in a clockwise direction starting. The bearing of a point is the line joining the centre of the compass through the point measured in degrees in a clockwise way from the north direction. The students should ideally have some experience of solving worded trigonometry questions in which diagrams are not given. Free tutorials and problems on solving trigonometric equations, trigonometric identities and formulas can also be found. Components of a vector. Level 4 - Creating scale diagrams and making accurate measurements of given situations. If you are just given the three distances AB, AC, BC, you can solve triangle ABC (i,e, find its angles) by standard trigonometry, but you can't possibly find the bearings, since those depend on the actual positions of points A, B, C with respect to the true north. Trigonometry is often used in real world applications, such as astronomy, architecture, engineering, music theory and geography. It therefore also plays an important role on your maths exam!. If AB= 8km and AC= 6km, what is the bearing of B from C? tanC = 8/6, so C = 53. COMPLETE THE GCSE MATHS TAKEAWAY AND GET YOUR GRADE. AB=BC=20cm. The trigonometry angles which are commonly used in trigonometry problems are 0°, 30°, 45°, 60° and 90°. Instructions Use black ink or ball-point pen. All the free maths worksheets were generated in seconds by Mathster! You can create your own maths worksheets very easily - take a free months trial subscription and see how easy Mathster makes it!. The answer to “Bearing of a Plane A plane flies 650 mph on a bearing of 175. com's quick multiple-choice quiz. I mean how can trigonometry can be used in real life situations like navigation, architecture, survey, astronomy etc. 6, blows against the. Click the mouse along the slider and watch the updating below for the bearing. In university maths it is much more common to give angles in radians rather than degrees. Determine how far south the tanker is from its starting point. It was on a crossroads. Trigonometry Challenge Give it a try! From a granite post, proceed 195 ft. - Lessons and worksheets suitable for the 9 - 1 GCSE Specification. At Cazoom Maths we provide engaging scale drawing, bearings maths and loci maths worksheets to help students calculate bearings and scale length with ease. The bearing of C from A is 135º. Khan Academy Trigonometry Video Iintroduction, Example, Another Example. We will also show the table where all the ratios and their respective angle's values are mentioned. A 25-mph wind, from a direction of 266. The diagram below, which is not drawn to scale, represents the positions of three mobile phone masts. Showing top 8 worksheets in the category - Trigonometry Bearings. Maths GCSE Bearings - collinbillet on TES; Bearings lesson - Boss Maths; Bearings using parallel lines - nem25 on TES ; Angle properties and bearings - pas1001 on TES; Bearings worksheets and Finding bearings - The Chalk Face; Calculating bearings - Maths4Everyone on TES; Bearings Challenges - solvemymaths. port A 25 km a Calculate the distance of the ship 390 port B to the nearer port. Find PowerPoint Presentations and Slides using the power of XPowerPoint. 9 Trigonometry (1) 9. Start studying Chapter 15 - Scale drawings, bearing and Trigonometry. Resources on trigonometry problems used in modular course 4 Tutorial on using GeoGebra to investigate trigonometric ratios Resources to help students with their understanding of slope - developed by the NCCA. (b) When Emma arrives at point B she changes direction and sails to point C on a bearing of 230° and one 1 km away. Frequently Asked Questions About Trigonometry An interactive tutorial which teaches the basics of. Angle CAB is the difference of those two bearings. Consider the following statements A: log 10 (10 x) > 0. (What they'd teach you if they had the time Book 2) - Kindle edition by Kevin Bennett. The trigonometric ratios such as sine, cosine and tangent of these angles are easy to memorize. Both topics of Pythagoras’ Theorem. Trigonometry is the study of triangles, which contain angles, of course. Trigonometry will then inform them of the distance which they need to travel. Start studying Chapter 15 - Scale drawings, bearing and Trigonometry. Analyze A Bearings Word Problem Using Trigonometric Ratios and the Law of Cosine. This means that most of the links on this page are not yet active. This tutorial contains a few. Melody and April go to the same school. To start practising, just click on any link. Best team of research edit my paper online writers makes best orders for students. 9km but not sure how to get to it) B) how far had the ship sailed from port to angle bay (answer is 21. Trigonometry and bearings [ 1 Answers ] Can you please tell me what does it mean when it says:- 'The difficulty with trigonometric problems involving bearings is dealing with those angles greater than 90 degrees whose trigonometric ratios have negative values. The angle of elevation from the top of the smaller of the two hills, to the the top of the taller one is 27º. The bearing of # from : is 018°T and from ; is 282°T. Trigonometry Here is a list of all of the skills that cover trigonometry! These skills are organised by year, and you can move your mouse over any skill name to preview the skill. Enter values three of the six sides and angles of the triangle and the other three values will be computed. Maths Made Easy gives you access to maths worksheets, practice questions and videos to help you revise. Pythagoras and Trigonometry Right-Angled Triangle Trigonometry. Trigonometry and Bearings Trigonometry in Right Triangles In right 4ABC, ACis called the hypotenuse. angle of elevation. Learning to solve right triangles provides the foundation you'll be using as you advance in trigonometry. Monthly payment and total interest are defined as:. Austin State University Fall 2019 Learning Objectives In any triangle ABCwith sides a, b, and c, and angles , , and. Mast Q is on a bearing of 100o from mast P and is 40km away. Linear algebra, calculus and statistics all use trig in one form or another. Math Help Forum Mathematics is concerned with numbers, data, quantity, structure, space, models, and change. Trigonometry is the study of triangles, which contain angles, of course. Trigonometry 2 - Sine, Cosine Rule, Area of 'Iriangle Two yachts Ieave from harbour H. Visit the post for more. Videos, online assessments, feedback tools, independent learning, printable worksheets and so much more are all included to h. 1 Answer by Expert Tutors. I think that math instructors have a duty to prepare students for that. The sheets present concepts in the order they are taught and give examples of their use. 6 miles bearing N27°E. Non-calculator trigonometry (Problem solving 1) 853. Math Math Math Classroom Teaching Math Gre Math Ks2 Maths Trigonometry Math Formulas Geometry Formulas Gcse Revision From our Maths poster range, the Types of Triangles Poster is a great educational resource that helps improve understanding and reinforce learning. appreciate the notion of space as a set of points with subsets of that set (space) having properties related to other mathematical systems; 2. It was on a crossroads. Find after 2 hours (a) the distance between the ships, (b) the bearing from the first ship to. 0 miles north, then 2. Trigonometry is often used in real world applications, such as astronomy, architecture, engineering, music theory and geography. angle of elevation. Trigonometry Solving Triangles: Bearing Problems 1) A bridge is to be built across a lake, from point B to point C in the figure shown. Our Key Stage 3 (KS3) maths eBooks comprise three principle sections. Reference : Maths for HK4B P. pdf: File Size: 40 kb: File Type: pdf. com, find free presentations research about O Level Bearings In Trigonometry PPT. Sine and Cosine Law (cont’d) Math Power 11 p. Literally, trigonometric equations concern themselves with "triangle measurement"; and trigonometry is a specialized branch of mathematics that deals mainly with the properties of triangles and the relationships between its parts. Given bearing from A to B is 75°. This is the first of three articles on the History of Trigonometry. Our worksheets present this essential information in an easily digestible format and give plenty of activities for students to practice calculating bearings. angle of depression. com, find free presentations research about Bearings In Trigonometry PPT. Founded in 2005, Math Help Forum is dedicated to free math help and math discussions, and our math community welcomes students, teachers, educators, professors, mathematicians, engineers, and scientists. If AB= 8km and AC= 6km, what is the bearing of B from C? tanC = 8/6, so C = 53. Trigonometry - Maths - Revision Videos. pdf Free Download Here Trigonometry - Hard Problems Q&A - MathGuy. BEARINGS AND TRIGONOMETRY The bearing of K from H 48km. Cosine Rule and Bearing Problem - GCSE and a-level revision video This video shows how to use the cosine rule to solve a problem involving bearings. Within the Trigonometry section of Revision Videos, you will find a wide range of videos covering: Bearings, Pythagoras Theorem, Radians, Sine, Cosine and Tangent and the Sine and Cosine Rules. 30 0 is expressed as 030 0. An oil tanker sails on a bearing of 135°( for 388km. Bearings My students have a melt-down when I give them a problem that involves trigonometry and bearings. These navigation problems use variables like speed and direction to form vectors for computation. Question 18. New York State Regents Trigonometry Score of at least 85. Mathematics (Linear) – 1MA0 BEARINGS Materials required for examination Items included with question papers Ruler graduated in centimetres and Nil millimetres, protractor, compasses, pen, HB pencil, eraser. Chegg is one of the leading providers of trigonometry help for college and high school students. I don't understand why the bearing from A back toward C is 180 degrees. From point A, the bearing to B is S 74° E and the bearing to C is S 28° E. They are simply one side of a right-angled triangle divided by another. IXL will track your score, and the questions will automatically increase in difficulty as you improve!. THE FIENDISH ANGLETRON TRIGONOMETRY and GEOMETRY. Example 1: Compass bearing of Y from X is N50°E. Tarrou teaches students an entire course on trigonometry from start to finish, and on top of that, provides a comprehensive and easy to understand introduction to polar coordinates, vectors, and complex numbers. angle of elevation. Year 9 - click here for your homework on Chapter 15 - Trigonometry. Question: AB is a vertical tower 30 metres high, C and D are points at the same level as its foot A. Then have a look at the diagram at the bottom of that page. Find to the nearest ten minutes the bearing of the slower boat from the faster at the end of one hour. 10A Trig Bearings FIN2013 Trigonometry - Bearings 1. Practical use of Trigonometry. Our worksheets present this essential information in an easily digestible format and give plenty of activities for students to practice calculating bearings. Read each question carefully before you begin answering it. In addition, the calculator shows the proof of the Pythagorean Theorem and then determines by numerical evaluation if the 2 sides and hypotenuse you entered are a right triangle using the Pythagorean Theorem. Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships between side lengths and angles of triangles. Five minutes later its bearing is 79 deg 43 mins. Having looked at true bearing and compass bearings, let us now look at some problems in bearings. How far is the boat from H? What is the bearing from H?. The drop-off point is. Directions and Bearings. The bearing of Q from P is 030° and PQ is 1200 m apart and hot air balloon is spotted vertically above Q at an angle of elevation of 21° from P. Trigonometry starts with a right-angled triangle: The longest side is always called the hypotenuse. An oil tanker sails on a bearing of 135°! for 388km. If AB= 8km and AC= 6km, what is the bearing of B from C? tanC = 8/6, so C = 53. Can you form some rules to help you remember how to calculate bearings. This new tool has a fully updated, clean and user-friendly interface. We will also show the table where all the ratios and their respective angle's values are mentioned. The first person sails due west for 40 km and the second person sails round 230° until he is due south of the first person. Terminal side of an angle - trigonometry. Find the top 100 most popular items in Amazon Books Best Sellers. To start practising, just click on any link. Masts P and R are 66km apart. How long is the wire in meters?. Bearings are usually given as a three-figure bearing. 1 The sine and cosine rules The sine rule and the cosine rule extend trigonometry to triangles which are not necessarily right-angled. THE FIENDISH ANGLETRON TRIGONOMETRY and GEOMETRY. In Chapter 5 students are asked to use the free open-source software Gnuplot to graph some functions. - A-Level teaching resources for Core 1, Core 2, Core 3, Core 4, Decision 1 and Statistics 1. Luckily, we’re on hand to help with GCSE Maths revision. the study of the properties of triangles and trigonometric functions and of their applications…. The following collection of resources have been assembled by the TES Maths Panel. Kevin pedalled his pushbike along a road for 4km in the direction S650E. The formulae given at the top the worksheet are exactly the same information as will be given in the exam, so rearranging them is up to you. Some navigation problems ask us to find the groundspeed of an aircraft using the combined forces of the wind and the aircraft. I think that math instructors have a duty to prepare students for that. Part 2 can be found here. how far is the hiker from the trailhead as the crow flies. Solution for Р3 (x, у)3у35х-4. Trignometry resources--video tutorials, interactive lessons and free calculators. Donʼt spend too long on one question. Since the solution to 24 from 7. I find it very helpful to see how these concepts are covered on Khan Academy, but unfortunately it does not seem like they are included in the trigonometry section. The bearing of C from A is 135º. I suspect this is because my school doesn't teach bearings very well at Key Stage 3 (up until recently it wasn't even on our scheme of work), so they never know which angle they're meant to be calculating. With an EdPlace account you'll be able to track and measure progress, helping each child achieve their best. For the diagram above, the bearing of C from A is 045 degrees and the bearing of C from B is 015 degrees. Bearings are a way of expressing the angle between two objects, and there is a specific set of rules about how bearings should be calculated and expressed. Videos, worksheets, 5-a-day and much more. angle of depression. If you are just given the three distances AB, AC, BC, you can solve triangle ABC (i,e, find its angles) by standard trigonometry, but you can't possibly find the bearings, since those depend on the actual positions of points A, B, C with respect to the true north. For any angle "θ": (Sine, Cosine and Tangent are often abbreviated to sin, cos and tan. Trigonometry and bearings [ 1 Answers ] Can you please tell me what does it mean when it says:- 'The difficulty with trigonometric problems involving bearings is dealing with those angles greater than 90 degrees whose trigonometric ratios have negative values. The topic is that we need to find the application of trigonometry on any one of the real life situations using 3-dimensional figures. 9% per hour. Posted by CharlieMm at. The trigonometric ratios such as sine, cosine and tangent of these angles are easy to memorize. Easier to grade, more in-depth and best of all 100% FREE! Kindergarten, 1st Grade, 2nd Grade, 3rd Grade, 4th Grade, 5th Grade and more!. Having looked at true bearing and compass bearings, let us now look at some problems in bearings. • Use trigonometric ratios, sine rule and cosine rule to find bearings between 2 points. The adjacent is the side that forms part of the required angle. Find the length of the line from B which is perpendicular to ACRemember to put "cm". Sine and cosine proof GCSE trigonometry. 210° 330° N E C S D W. I then walk 5 km. The bearing from B to C is S 41° W. US http://www. The tend to sneak their way into several key topics, most notably angle facts, construction and trigonometry. The other way, on the right below, measures the angle clockwise from due north. Loci & Trigonometry of non-right angled triangles. After 30 minutes, the student has calmed down enough to get their bearing and head back to their apartment. The vertices are labelled using capital letters. there is even a warning if there are no solutions, two solutions, or if you need to check the angles. BELOW IS A LIST OF TOPICS WITH EXAM QUESTIONS ATTACHED. This website and its content is subject to our Terms and Conditions. Trigonometry problems multiple choice questions (MCQs), trigonometry problems quiz answers to learn online college courses for math classes. Sine Rule Proof. Trigonometry Right Triangle Word Problems 1. Calculate the distance the ship is east of its starting position, giving your answer to 1 d. Bearings measure the direction of one object to another. I'll attempt to include enough information that those familiar with plane trigonometry can derive additional results if required. 2 miles bearing S63°E to reach point B. Powered by Create your own unique website with customizable templates. 600m further along the road, the bearing of the pylon in 296 degrees. The trigonometric ratios such as sine, cosine and tangent of these angles are easy to memorize. Email: [email protected] Bearings are a way of expressing the angle between two objects, and there is a specific set of rules about how bearings should be calculated and expressed. Affordable Prices, Advanced Quality Control. High school students who are pursuing a math-intensive degree may wish to take this trigonometry course in the eighteen weeks as it is laid out and follow it with another semester-long math course, such as. Find x and H in the right triangle below. Right Triangle Trig Part II 3. Example 1: Compass bearing of Y from X is N50°E. _trigonometry_-_right-angled_triangles. Advanced Trade Math Annotated Instructor’s Guide MODULE OVERVIEW This module provides trainees with advanced practice in geometry, ratios, trigonometry, and algebra. The grade 11 mathematics trigonometry worksheet tests the sine, cosine and area rules learnt and determines whether students can apply it to two-dimensional (2D) questions. BEARINGS AND TRIGONOMETRY The bearing of K from H 48km. Nat 5 Maths – Using Bearings with Trigonometry October 7, 2015 October 7, 2015 / stevengraham123 / Leave a comment A short video tutorial showing you how to tackle trigonometry questions involving bearings. Trigonometry worksheet 5 contains questions on the sine rule. The numbers in brackets are the true bearing readings. Calculate the distance from point Y to point Z. Trigonometry was written by Patricia and is associated to the ISBN: 9780321671776. Receive All Updated And New Maths Lessons By E-mail Enter your e-mail address below and be the first to receive all new and updated lessons and resources. What is a bearing in trigonometry? i am a freshman in sophmore math which is geometry yet we are doing trigonometry makes sense right?!?! anyway the question reads: Three ships are situated as follows: A is 225 miles north of C and B is 375 miles due east of C. From point A, the bearing to B is S 74° E and the bearing to C is S 28° E. Learn vocabulary, terms, and more with flashcards, games, and other study tools. The name comes from the Greek words for triangle (trigonon – three angles) and measure (metron). Degrees can be converted to radians using the above formula, but it will be very convenient for you to know some standard conversions. More specifically, trigonometry is about right-angled triangles, where one of the internal angles is 90°. How to solve bearing problems in trigonometry Personal essay rubrick rice university essay examples research paper for science fair sample vending business plan pdf homework picture cartoon starting wedding planning business research paper topics on cancer slader homework helper. School students can use the free math lessons to help understand their school homework and prepare for exams and assignments. A train travels on a bearing of ! 25° ! until it is 285km south of its starting point. If you walk from O in the direction shown in the diagram, you are walking on a bearing of 110 °. In 4ABC, AB= c, BC= a, and AC= b. 130 0 is expressed as 130 0. After 30 minutes, the student has calmed down enough to get their bearing and head back to their apartment. The trigometric functions have a number of practical applications in real life and also help in the solutions of problems in many branches of mathematics. The bearings from a point P of two points A and B are 34 0 and 124 0 and their distances from P are 230 m and 760 m respectively. The main functions in trigonometry are Sine, Cosine and Tangent. Shed the societal and cultural narratives holding you back and let free step-by-step Blitzer Algebra and Trigonometry textbook solutions reorient your old paradigms. From the standpoint of an observer looking down from above this is 145 degrees counterclockwise. They can be downloaded for free by registering on the TES website. They are simply one side of a right-angled triangle divided by another. A barge is 12 km south of the lobster boat. How far west has it travelled? 2. This is Sydney International Airport:. east, then along a bearing of S32 ° E for 260 ft. One of the most common uses for trigonometry, or trig, is in mathematics. A collection of videos, activities and worksheets that are suitable for A Level Maths. The remaining have only answered 1 question and that isn't always the same question for each student. It looks like this computer has lost access to the internet. I have a algebra test pretty soon and even though I have been studying algebra seriously, there are still a few parts that cause a lot of stress, such as bearing problems sample trigonometry and conversion of units especially. between what two points. angle of depression. For an illustration of these basic trigonometry concepts with further explanations, please click here. Question 18. A) how far south had the ship sailed before turning (answer is 15. Trigonometry • 1 Naming Sides • 2 Trigonometry Ratios • 3 Finding Sides • 4 Finding Angles • 5 Angles of Elevation & Depression • 6 Using Trigonometry to Solve Problems • 7 Bearings Basics • 8 Solving Bearings Problems • 9 Trigonometry With Obtuse Angles • 10 Area of Non Right-Angled Triangles • 11 Sine Rule For Sides.