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Apply Trigonometry Knowledge to 3D Shapes

In this worksheet, students will be able to apply their knowledge of trigonometry to 3D shapes.

'Apply Trigonometry Knowledge to 3D Shapes' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, OCR, Pearson Edexcel,

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation Triangle Mensuration

Difficulty level:  

Worksheet Overview

man on a mountain                  sailing           


How can you find the height of this mountain?

How can this mountaineer draw an accurate map?

How did sailors navigate before GPS?

How can computers rotate images so that they can be viewed from many different directions?



They look at angles and sides of triangles and make connections between them.

This is pretty cool stuff really.


This is called Trigonometry.   A lot of the times trigonometry is applied in 3D.

Trigonometry is used to help solve problems within right angled triangles.

Trigonometry ratios - recap

Sin ratio cosine ratiotan ratio  



                          cuboid with triangle drawn in

1. Draw in the right angled triangle as shown in the example.  Then if it is helpful draw it out in 2 dimensions.

2. Label the triangles

3. Apply the correct trig ratio

4.  We have the opposite 10 cm and the adjacent 20 cm, therefore the tan ratio.

5.  10 ÷ 20 = 0.5 then tan-1 0.5 = 26.6° correct to one decimal place.


So time to quit the computer game (although trigonometry is used to help create them) and have a go at applying your knowledge.



Note:  Don't round up your answers until you have worked through the whole problem otherwise your answer may differ quite a bit.

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