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- 3.2 Trigonometry.
- 3.3 Trigonometry Applications.
- 3.5 Unit Circle and Exact Values.

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Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.

- Common Trig Ratios A self-marking exercise on finding the exact values of sine, cosine and tangent of special angles.
- Common Trig Ratios Video You may not realise that it is possible to find sin60° or tan45° without a calculator. This video is to help you do the online, self-marking exercise.
- 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.
- 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.
- Which Side? Arrange the diagrams in groups depending on whether the arrow is pointing to the opposite, adjacent or hypotenuse.
- Pythagoras An online exercise to test your understanding of and ability to apply Pythagoras' Theorem.
- Make Them Right Arrange the measurements next to the sides of the triangles so that each diagram is correct according to Pythagoras' Theorem.
- Pythagoras' Theorem Video The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides.
- 3D Trigonometry Presentation A slide presentation (a poem) introducing using trigonometry (including Pythagoras' Theorem) to find lengths and angles on three dimensional shapes.
- Three Dimensional Trigonometry Video When you have mastered trigonometry in two dimensions it is time to practise solving three-dimensional problems.
- Triangle Solver Provide and three measurements for a triangle and this application will work out the remaining sides, angles and area.

Here are some exam-style questions on this topic:

- "
*The diagram (not drawn to scale) shows a right-angled triangle.*" ... more - "
*An isosceles triangle shaped frame is made from four pieces of metal. The frame has a height of 8 metres and a base of length 12 metres.*" ... 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. - "
*The diagram shows a right-angled triangle and a semicircle. The straight side of the semicircle is the same length as the longest side of the triangle.*" ... more - "
*The diagram shows a trapezium where the sides AC and BD are parallel.*" ... more - "
*Four copies of a green right-angled triangle are used to enclose a yellow square.*" ... 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). - "
*Find the exact value of tan45° × sin30° × cos30°*" ... more - "
*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 - "
*(a) Write down the exact value of \(\tan 60^o\).*" ... more - "
*Rectangle ABCD is the horizontal base of a trapezoidal prism ABCDEFGH.*" ... more - "
*The area of triangle ABC (not drawn to scale) is*" ... more - "
*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 - "
*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 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. Lengths are given in centimetres.*" ... more - "
*Christine owns a four sided piece of land shown in the diagram below as ABCD. The length of BC is 180 m, the length of CD is 70 m, the length of AD is 90 m, the size of angle BCD is 82° and the size of angle BAD is 102°. The diagram is not to scale*" ... 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 - "
*The cosine of acute angle \( \alpha \) is \( \frac{1}{ \sqrt 5} \)*" ... 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:

**Speed Circles**

Find the diameters of the circles in the corners of the square. more**Tan 22.5**

Find an exact value for tan 22.50 without using a calculator. more**Three Right Triangles**

Calculate the lengths of the unlabelled sides of these right-angled triangles. more**Trig Blot**

Find all the measurements of the given triangle. more

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

This Scheme of Learning was produced by White Rose Maths and is used here with permission granted on 30th June 2021.