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Trigonometry: Finding Angles

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

'Trigonometry: Finding Angles' worksheet

Key stage:  KS 4

Curriculum topic:  Geometry and Measures

Curriculum subtopic:  Apply Pythagoras' Theorem and Trigonometric Ratios to Find Angles and Lengths in 2D Figures

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

This worksheet is about calculating angles using trigonometry in right-angled triangles.

 

Remember: sin x = opp , cos x = adj , tan x = opp
hyp hyp adj

 

Examples : Find the angle, x, in degrees:

You know
hypotenuse = 5.8;
opposite side = 5;
sin x = 5
5.8
x = sin-1 5
5.8
On your calculator:
x = shift sin (5 ÷ 5.8)
= 59.5 (1 d.p.)
You know
hypotenuse = 6.3;
adjacent side = 2;
cos x = 2
6.3
x = cos-1 2
6.3
On your calculator:
x = shift cos (2 ÷ 6.3)
71.5 (1 d.p.)
You know
opposite side = 3;
adjacent side = 4;
tan x = 3
4
x = tan-1 3
4
On your calculator:
x = shift tan (3 ÷ 4)
36.9 (1 d.p.)

Find the angle marked x, in degrees, to 1 decimal place.

(Just write the number of degrees)

 

x =
 

Find the angle marked x, in degrees, to 1 decimal place.

 

x =
 

Find the angle marked x, in degrees, to 1 decimal place.

 

x =
 

Find the angle marked x, in degrees, to 1 decimal place.

 

 

x =
 

Find the angle marked x, in degrees, to 1 decimal place.

 

 

x =
 

Find the angle marked x, in degrees, to 1 decimal place.

 

x =
 

Find the angle marked x, in degrees, to 1 decimal place.

 

 

x =
 

Find the angle marked x, in degrees, to 1 decimal place.

 

x =
 

Find the angle marked x, in degrees, to 1 decimal place.

 

x =
 

Find the angle marked x, in degrees, to 1 decimal place.

 

x =
 
  • Question 1

Find the angle marked x, in degrees, to 1 decimal place.

(Just write the number of degrees)

 

x =
 
CORRECT ANSWER
54.5
EDDIE SAYS
x = sin-1(7/8.6)
  • Question 2

Find the angle marked x, in degrees, to 1 decimal place.

 

x =
 
CORRECT ANSWER
11.3
EDDIE SAYS
x = tan-1(2/10)
  • Question 3

Find the angle marked x, in degrees, to 1 decimal place.

 

x =
 
CORRECT ANSWER
15.9
EDDIE SAYS
x = tan-1(2/7)
  • Question 4

Find the angle marked x, in degrees, to 1 decimal place.

 

 

x =
 
CORRECT ANSWER
33.7
EDDIE SAYS
x = sin-1(4/7.2)
  • Question 5

Find the angle marked x, in degrees, to 1 decimal place.

 

 

x =
 
CORRECT ANSWER
35.5
EDDIE SAYS
x = tan-1(5/7)
  • Question 6

Find the angle marked x, in degrees, to 1 decimal place.

 

x =
 
CORRECT ANSWER
41.0
EDDIE SAYS
x = cos-1(8/10.6)
  • Question 7

Find the angle marked x, in degrees, to 1 decimal place.

 

 

x =
 
CORRECT ANSWER
49.5
EDDIE SAYS
x = sin-1(7/9.2)
  • Question 8

Find the angle marked x, in degrees, to 1 decimal place.

 

x =
 
CORRECT ANSWER
53.1
EDDIE SAYS
x = tan-1(4/3)
  • Question 9

Find the angle marked x, in degrees, to 1 decimal place.

 

x =
 
CORRECT ANSWER
59.5
EDDIE SAYS
x = sin-1(5/5.8)
  • Question 10

Find the angle marked x, in degrees, to 1 decimal place.

 

x =
 
CORRECT ANSWER
67.1
EDDIE SAYS
x = sin-1(7/7.6)
---- OR ----

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