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Solve Trigonometry Problems

In this worksheet, students will apply Pythagoras' Theorem and trigonometry within 3D shapes. A requirement of higher level maths is to apply more than one skill within the same question.

'Solve Trigonometry Problems' 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


Ever wanted to fly a fast jet or passenger aircraft.  Well if you do you will need to be good at trigonometry


Angles and distances are an everyday part of a pilots jobs.

If you ask a pilot if they are happy in their jobs, they would probably say it has its ups and downs.


Engineers and designers would also use trigonometry a great deal in their work.


Lets recap on your trigonometry ratios.

Sin ratiocos ratio 

oh and would you believe it pythagoras our mate Pythagoras gets in on the act.  He can't help himself can he.


Pythagoras' Theorem

a² + b² = c²

I wonder if pilots ever think about him when the fly over Greece.

The trig ratios are often combined with Pythagoras's Theorem when solving problems relating to right angled triangles.


Lets have a go


 cuboidcuboid with 3d annotationcuboid with 3d annotation

Figure 1 just asks the question, that may well be all that you are given.

Figure 2 Draw in the right angled triangle.

Figure 3 Mark in the angle.  Remember it is the middle letter A.


Pythagoras' Theorem has also been applied in figure 3 to find the length of the diagonal.  We need this before we can calculate the angle.

30 cm² + 10 cm² = √1000 = 31.622..... cm

Mark this on the diagram to help see the trig ratio that you need.

To find angle A you have the opposite side and now the adjacent to help you.

20 ÷ 31.6222 = 0.63246...... tan-1 0.63246 = 32.3° correct to 1 decimal place.


There is quite a lot to take in here so take it one step at a time.


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