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  2. Year 9
  3. Lines, Angles and Degrees
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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:  

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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 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.)

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

(just write the number)

 

 

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

(just write the number)

 

 

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

(just write the number)

 

 

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

(just write the number)

 

 

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

(just write the number)

 

 

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

(just write the number)

 

 

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

(just write the number)

 

 

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

(just write the number)

 

 

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

(just write the number)

 

 

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

(just write the number)

 

 

  • ANSWERS
  • Question 1

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

(just write the number)

 

 

CORRECT ANSWER
36.9
EDDIE SAYS
θ = sin-1(3/5)
  • ANSWERS
  • Question 2

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

(just write the number)

 

 

CORRECT ANSWER
36.9
EDDIE SAYS
θ = tan-1(3/4)
  • ANSWERS
  • Question 3

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

(just write the number)

 

 

CORRECT ANSWER
53.1
EDDIE SAYS
θ = tan-1(4/3)
  • ANSWERS
  • Question 4

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

(just write the number)

 

 

CORRECT ANSWER
26.4
EDDIE SAYS
θ = sin-1(4/9)
  • ANSWERS
  • Question 5

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

(just write the number)

 

 

CORRECT ANSWER
38.9
EDDIE SAYS
θ = cos-1(7/9)
  • ANSWERS
  • Question 6

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

(just write the number)

 

 

CORRECT ANSWER
51.3
EDDIE SAYS
θ = tan-1(5/4)
  • ANSWERS
  • Question 7

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

(just write the number)

 

 

CORRECT ANSWER
45.6
EDDIE SAYS
θ = sin-1(5/7)
  • ANSWERS
  • Question 8

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

(just write the number)

 

 

CORRECT ANSWER
38.1
EDDIE SAYS
θ = tan-1(4/5.1)
  • ANSWERS
  • Question 9

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

(just write the number)

 

 

CORRECT ANSWER
41.8
EDDIE SAYS
θ = sin-1(6/9)
  • ANSWERS
  • Question 10

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

(just write the number)

 

 

CORRECT ANSWER
55.5
EDDIE SAYS
θ = cos-1(5.1/9)
---- OR ----

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