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These are the Transum resources related to the statement: "Use of sine, cosine and tangent ratios to find the sides and angles of right-angled triangles. use of the sine rule, cosine rule and the sine formula for finding the area of a triangle".

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

- Triangle Solver Provide and three measurements for a triangle and this application will work out the remaining sides, angles and area.
- Trigonometry 20 trigonometry questions in an online, self marking exercise.
- Trigonometry Advanced A self-marking exercise on the sine rule, cosine rule and the sine formula for finding the area of a triangle.
- Which Side? Arrange the diagrams in groups depending on whether the arrow is pointing to the opposite, adjacent or hypotenuse.

Here are some exam-style questions on this statement:

- "
*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 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). - "
*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 - "
*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 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 - "
*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 shown the origin O (0,0) and a fixed point A(10,2). The point P moves along the horizontal line \(y = 8\).*" ... more

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

Syllabus guidance and clarification:

In all areas of this topic, students should be encouraged to sketch well-labelled diagrams to support their solutions.

This section does not include the ambiguous case of the sine rule.

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