 # Finding a Side Length Using Trigonometry (2)

In this worksheet, students use trigonometry to calculate a side length in right-angled triangles. Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Solve Right-Angled Triangle Problems

Difficulty level:   ### 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. 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. 5.09
EDDIE SAYS
x = 7 ÷ tan54°
• Question 2

Using trigonometry, calculate the side length x to 3 sig. figs. 10.1
EDDIE SAYS
x = 7 ÷ sin44°
• Question 3

Using trigonometry, calculate the side length x to 3 sig. figs. 31.2
EDDIE SAYS
x = 17 ÷ cos57°
• Question 4

Using trigonometry, calculate the side length x to 3 sig. figs. 32.2
EDDIE SAYS
x = 27 ÷ sin57°
• Question 5

Using trigonometry, calculate the side length x to 3 sig. figs. 9.09
EDDIE SAYS
x = 14 ÷ tan57°
• Question 6

Using trigonometry, calculate the side length x to 3 sig. figs. 7.51
EDDIE SAYS
x = 6 ÷ cos37°
• Question 7

Using trigonometry, calculate the side length x to 3 sig. figs. 8.90
EDDIE SAYS
x = 6 ÷ tan34°
• Question 8

Using trigonometry, calculate the side length x to 3 sig. figs. 27.4
EDDIE SAYS
x = 12 ÷ cos64°
• Question 9

Using trigonometry, calculate the side length x to 3 sig. figs. 13.4
EDDIE SAYS
x = 12 ÷ sin64°
• Question 10

Using trigonometry, calculate the side length x to 3 sig. figs. 6.30
EDDIE SAYS
x = 5.1 ÷ tan39°
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