# Trigonometry: Finding Angles

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

Key stage:  KS 4

Curriculum topic:  Geometry and Measures

Difficulty level:

### 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
x = shift sin (5 ÷ 5.8)
= 59.5 (1 d.p.)
You know
hypotenuse = 6.3;
 cos x = 2 6.3
 x = cos-1 2 6.3
x = shift cos (2 ÷ 6.3)
71.5 (1 d.p.)
You know
opposite side = 3;
 tan x = 3 4
 x = tan-1 3 4
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 =
54.5
EDDIE SAYS
x = sin-1(7/8.6)
• Question 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

x =