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Finding the Angle Using Trigonometry

In this worksheet, students use trigonometry to calculate the angle in right-angled triangles.

'Finding the Angle Using Trigonometry' worksheet

Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Solve Right-Angled Triangle Problems

Difficulty level:  

Worksheet Overview

In a right-angled triangle, the sides and the angles are connected by three trigonometric ratios.



The three trig ratios are:



A quick way to remember this is to memorise the word




Using trigonometry, calculate the angle θº to 3 sig. figs.




Label the sides adjacent, opposite and hypotenuse in relation to the angle θº.

The given sides are the adjacent and the hypotenuse.




The correct trig ratio is COS.


Set up the trig equation to get:

cos θ = 3/5 = 3 ÷ 5 = 0.6

θ = cos-1 (0.6)

θ = 53.1º (3 s.f.)

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