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Finding a Side Length Using Trigonometry (2)

In this worksheet, students use trigonometry to calculate a side length in right-angled triangles.

'Finding a Side Length Using Trigonometry (2)' 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

 

Example

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.)

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

 

 

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

  

 

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

 

 

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

 

 

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

 

 

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

 

 

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

 

 

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

 

 

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

 

 

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

 

 

  • Question 1

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

 

 

CORRECT ANSWER
5.09
EDDIE SAYS
x = 7 ÷ tan54°
  • Question 2

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

  

 

CORRECT ANSWER
10.1
EDDIE SAYS
x = 7 ÷ sin44°
  • Question 3

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

 

 

CORRECT ANSWER
31.2
EDDIE SAYS
x = 17 ÷ cos57°
  • Question 4

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

 

 

CORRECT ANSWER
32.2
EDDIE SAYS
x = 27 ÷ sin57°
  • Question 5

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

 

 

CORRECT ANSWER
9.09
EDDIE SAYS
x = 14 ÷ tan57°
  • Question 6

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

 

 

CORRECT ANSWER
7.51
EDDIE SAYS
x = 6 ÷ cos37°
  • Question 7

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

 

 

CORRECT ANSWER
8.90
EDDIE SAYS
x = 6 ÷ tan34°
  • Question 8

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

 

 

CORRECT ANSWER
27.4
EDDIE SAYS
x = 12 ÷ cos64°
  • Question 9

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

 

 

CORRECT ANSWER
13.4
EDDIE SAYS
x = 12 ÷ sin64°
  • Question 10

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

 

 

CORRECT ANSWER
6.30
EDDIE SAYS
x = 5.1 ÷ tan39°
---- OR ----

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