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Mixed Trigonometry Questions

In this worksheet, students use trigonometry to calculate side lengths and angles in right-angled triangles.

'Mixed Trigonometry Questions' worksheet

Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Solve Right-Angled Triangle Problems

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

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

SOHCAHTOA

In this worksheet, you will be told to give your answers to 3 significant figures (3sf). You also don't need to worry about the units for these questions.

 

Example 1

Using trigonometry, calculate the side length x to 3 sig. figs.

 

 

Answer

Label the sides adjacent, opposite and hypotenuse in relation to the given angle 34º.

The given sides are the opposite (x) and the hypotenuse (8).

SOHCAHTOA

 

The correct trig ratio is SIN.

 

Set up the trig equation to get:

sin34º = x/8

x/8 = sin34º

x = 8 sin34º

x = 8 x  0.559192903....

x = 4.47 (3 s.f.)

 

Example 2

Using trigonometry, calculate the side length x to 3 sig. figs.

 

 

Answer

Label the sides adjacent, opposite and hypotenuse in relation to the given angle 54º.

The given sides are the hypotenuse (x) and the adjacent (7).

SOHCAHTOA

 

The correct trig ratio is COS.

 

Set up the trig equation to get:

cos54º = 7/x

xcos54º = 7

x = 7/cos54º

x = 7 ÷  0.587785252....

x = 11.9 (3 s.f.)

  

Example 3

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

 

 

Answer

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

The given sides are the adjacent and the hypotenuse.

 

SOHCAHTOA

 

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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