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These are the Transum resources related to the statement: "Understand and use the definitions of sine, cosine and tangent for all arguments; the sine and cosine rules; the area of a triangle in the form ½*ab*sin(C); Work with radian measure, including use for arc length and area of sector".

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

- Numbasics A daily workout strengthening your ability to do the basic mathematical operations efficiently.
- Which Side? Arrange the diagrams in groups depending on whether the arrow is pointing to the opposite, adjacent or hypotenuse.
- Trigonometry Video The basic trigonometric ratios are sine, cosine and tangent and are used to find the lengths of sides and the size of angles in right-angled triangles.
- Trigonometry Sine, cosine and tangent ratios are used to find sides and angles in right-angled triangles.
- Trigonometry Advanced A self-marking exercise on the sine rule, cosine rule and the sine formula for finding the area of a triangle.

Here are some exam-style questions on this statement:

- "
*The diagram (not drawn to scale) shows a right-angled triangle.*" ... more - "
*An arborist sights the top of a tree using a clinometer and reads the angle of elevation to be 29*" ... more^{o}. Her clinometer is 28 metres from the base of the tree and is on a tripod making it 1.5 metres above ground level. - "
*Here is triangle PQR:*" ... more - "
*The diagram shows a trapezium where the sides AC and BD are parallel.*" ... more - "
*Triangle ABC has a right angle at C.*" ... more - "
*Neung is at Bangkok's Suvarnabhumi Airport watching the planes take off. He observes a plane that is at an angle of elevation of 25*" ... more^{o}from where he is standing at point N. The plane is at a height of 390 metres as can be seen in the following diagram (not to scale). - "
*Consider the triangle ABC where AB=17cm, AC=14cm and the angle BAC = 118*" ... more^{o}. Find the length of BC. - "
*The angle marked \(x\) in the diagram below is obtuse. Find the value of \(x\)*" ... more - "
*The Tamarack triathlon race consists of swimming, cycling and running. Competitors swim from A to B, then cycle from B to C and finally run from C back to A.*" ... more - "
*Rectangle ABCD is the horizontal base of a trapezoidal prism ABCDEFGH.*" ... more - "
*The area of triangle ABC (not drawn to scale) is*" ... more - "
*The diagram shows parallelogram ABCD in which AD = \(x\) cm, DE = 12 cm and angle ABC = 30°*" ... more - "
*In triangle ABC, AB = 7cm and AC = 9cm. The area of the triangle is 20cm*" ... more^{2}. - "
*ABC is a triangular car park on horizontal ground. The length of AB is 90m and the length of AC is 65m. The size of angle BCA is 68*" ... more^{o}. - "
*The diagram (not to scale) shows a quadrilateral made up of a number of triangles.*" ... more - "
*Calculate the length of the side marked \(x\).*" ... more - "
*In the diagram of triangle ABC (not to scale) D is a point on BC.*" ... more - "
*The diagram, not drawn to scale, shows a quadrilateral ABCD.*" ... more - "
*The diagram shows a circle with a minor sector shaded blue and a major sector shaded yellow.*" ... more - "
*In triangle ABC, the length of AB = 5cm, AC = 13cm and \( \cos B \hat AC = \frac18 \).*" ... more - "
*In the diagram above (not drawn to scale), AB=12mm, BC=8mm and angle ABC=123*" ... more^{o} - "
*The following diagram shows part of a circle with centre O and radius 10cm.*" ... more - "
*The diagram below shows triangle ABC and the lengths of its sides. It is known that the cosine of angle \(C\hat{A}B\) is one third.*" ... more - "
*The diagram shows quadrilateral ABCD.*" ... more - "
*A builder marks out three points A, B and C on the ground such that AB = 11m , AC = 15m and angle BAC = 124*" ... more^{o}. - "
*Melissa has a webcam on the top of her computer screen. She has the zoom level adjusted so that that her head is framed nicely in the image produced. The diagram shows the setup.*" ... more - "
*A drone flying test course is in the shape of a triangle, ABC, with AB = 400m , BC = 600m and angle ABC = 44*" ... more^{o}. The course starts and finishes at point A. - "
*The diagram shows a circle of radius 8.6cm with points ABCD on the circumference of the circle.*" ... more - "
*Emma sails in a small dinghy from point A in a straight line to a buoy at point B. She is moving at an average speed of 19 km/h, for 6 minutes, on a bearing of 125°.*" ... more - "
*The diagram shows the positions of three towns, Aberville (A), Buchus (B) and Clipton(C).*" ... more - "
*The diagram shown the origin O (0,0) and a fixed point A(10,2). The point P moves along the horizontal line \(y = 8\).*" ... more

Here are some Advanced Starters on this statement:

**Pizza Slice**

A problem which can be solved by considering the areas of a triangle and a sector of a circle. more**Tansum**

Find the sum of the tangents of angles on a straight line. more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

This video on Radians, Lengths of Arcs and Areas of Sectors is from Revision Village and is aimed at students taking the IB Mathematics Analysis and Approaches SL and HL courses.

This video on Solving Trig Functions and Equations is from Revision Village and is aimed at students taking the IB Maths AA SL/HL course.

How do you teach this topic? Do you have any tips or suggestions for other teachers? It is always useful to receive feedback and helps make these free resources even more useful for Maths teachers anywhere in the world. Click here to enter your comments.