\( \DeclareMathOperator{cosec}{cosec} \)

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

- Make Them Right Arrange the measurements next to the sides of the triangles so that each diagram is correct according to Pythagoras' Theorem.
- 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.
- 3D Trigonometry Presentation A slide presentation (a poem) introducing using trigonometry (including Pythagoras' Theorem) to find lengths and angles on three dimensional shapes.
- Trigonometry in 3D Calculate the lengths of sides and the size of angles in three dimensional shapes.
- Three Dimensional Trigonometry Video When you have mastered trigonometry in two dimensions it is time to practise solving three-dimensional problems.

Here are some exam-style questions on this statement:

- "
*\(ABC\) is a right-angled triangle.*" ... more - "
*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 - "
*Work out the value of \(x\), the length in centimetres of one of the sides of this right-angled triangle.*" ... more - "
*ABC is a right-angled triangle as shown in the diagram below. Calculate the length of AB giving your answer correct to three significant figures.*" ... 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 - "
*Taptaya Park Tower is over two hundred metres tall. There is a zip wire from the observation deck to a point on the ground 550 metres away in a northerly direction.*" ... 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). - "
*A square has sides of length \(x\) cm.*" ... 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 diagram shows a rectangular-based pyramid, TABCD (not drawn to scale).*" ... 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 gradient of the line joining the origin to the point A is \(\frac12\)*" ... more

Here are some Advanced Starters on this statement:

**Coordinate Distance**

Find k given that(-2,k) is 13 units away from (10,9) more**Speed Circles**

Find the diameters of the circles in the corners of the square. more

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

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