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Trigonometry and Right-Angled Triangles

In this worksheet, students sketch right-angled triangles from the given data and then use trigonometry to answer the questions.

'Trigonometry and Right-Angled Triangles' 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

A sketch can be drawn from the given information to help you answer trigonometrical questions.

The sketch does not need to be accurate as it is just there to show you the position of the sides in relation to the angles (opposite, adjacent, hypotenuse)

 

Example

Triangle ABC has a right angle at B.

AB = 10 cm

∠ACB = 22.5º

After sketching the triangle, use trigonometry to calculate the length of the side AC.

 

Answer

 Sketch the triangle roughly.

 

 

Set up the trig equation using the sketch.

 

sin 22.5º = 10/AC

AC = 10/sin22.5º

AC = 26.1 cm

Triangle ABC has a right angle at B.

 

AB = 10 cm

 

∠ACB = 22.5º

 

After sketching the triangle, use trigonometry to calculate the length of the side BC.

 

(Give your answer to 3 sig. figs. and just write the number)

Triangle ABC has a right angle at B.

 

AB = 6.1 cm

 

∠ACB = 30º

 

After sketching the triangle, use trigonometry to calculate the length of the side AC.

 

(Give your answer to 3 sig. figs. and just write the number)

Triangle ABC has a right angle at B.

 

AB = 13 cm

 

∠ACB = 32º

 

After sketching the triangle, use trigonometry to calculate the length of the side AC.

 

(Give your answer to 3 sig. figs. and just write the number)

Triangle ABC has a right angle at B.

 

AC = 13 cm

 

∠ACB = 32º

 

After sketching the triangle, use trigonometry to calculate the length of the side AB.

 

(Give your answer to 3 sig. figs. and just write the number)

Triangle ABC has a right angle at B.

 

AC = 13 cm

 

∠ACB = 32º

 

After sketching the triangle, use trigonometry to calculate the length of the side BC.

 

(Give your answer to 3 sig. figs. and just write the number)

Triangle ABC has a right angle at B.

 

AC = 32 cm

 

∠CAB = 54.5º

 

After sketching the triangle, use trigonometry to calculate the length of the side BC.

 

(Give your answer to 3 sig. figs. and just write the number)

Triangle ABC has a right angle at B.

 

AC = 13.5 cm

 

∠CAB = 45º

 

After sketching the triangle, use trigonometry to calculate the length of the side AB.

 

(Give your answer to 3 sig. figs. and just write the number)

Triangle DEF has a right angle at E.

 

DE = 13.5 cm

 

∠EDF = 54º

 

After sketching the triangle, use trigonometry to calculate the length of the side EF.

 

(Give your answer to 3 sig. figs. and just write the number)

Triangle DEF has a right angle at E.

 

DE = 13.5 cm

 

∠EFD = 54º

 

After sketching the triangle, use trigonometry to calculate the length of the side EF.

 

(Give your answer to 3 sig. figs. and just write the number)

Triangle DEF has a right angle at E.

 

FE = 6.95cm

 

∠EFD = 25.8º

 

After sketching the triangle, use trigonometry to calculate the length of the side DF.

 

(Give your answer to 3 sig. figs. and just write the number)

  • Question 1

Triangle ABC has a right angle at B.

 

AB = 10 cm

 

∠ACB = 22.5º

 

After sketching the triangle, use trigonometry to calculate the length of the side BC.

 

(Give your answer to 3 sig. figs. and just write the number)

CORRECT ANSWER
24.1
EDDIE SAYS
10/tan22.5°
  • Question 2

Triangle ABC has a right angle at B.

 

AB = 6.1 cm

 

∠ACB = 30º

 

After sketching the triangle, use trigonometry to calculate the length of the side AC.

 

(Give your answer to 3 sig. figs. and just write the number)

CORRECT ANSWER
12.2
EDDIE SAYS
6/sin30°
  • Question 3

Triangle ABC has a right angle at B.

 

AB = 13 cm

 

∠ACB = 32º

 

After sketching the triangle, use trigonometry to calculate the length of the side AC.

 

(Give your answer to 3 sig. figs. and just write the number)

CORRECT ANSWER
24.5
EDDIE SAYS
13/sin32°
  • Question 4

Triangle ABC has a right angle at B.

 

AC = 13 cm

 

∠ACB = 32º

 

After sketching the triangle, use trigonometry to calculate the length of the side AB.

 

(Give your answer to 3 sig. figs. and just write the number)

CORRECT ANSWER
6.89
EDDIE SAYS
13sin32°
  • Question 5

Triangle ABC has a right angle at B.

 

AC = 13 cm

 

∠ACB = 32º

 

After sketching the triangle, use trigonometry to calculate the length of the side BC.

 

(Give your answer to 3 sig. figs. and just write the number)

CORRECT ANSWER
11.0
EDDIE SAYS
13cos32°
  • Question 6

Triangle ABC has a right angle at B.

 

AC = 32 cm

 

∠CAB = 54.5º

 

After sketching the triangle, use trigonometry to calculate the length of the side BC.

 

(Give your answer to 3 sig. figs. and just write the number)

CORRECT ANSWER
26.1
EDDIE SAYS
32sin54.5°
  • Question 7

Triangle ABC has a right angle at B.

 

AC = 13.5 cm

 

∠CAB = 45º

 

After sketching the triangle, use trigonometry to calculate the length of the side AB.

 

(Give your answer to 3 sig. figs. and just write the number)

CORRECT ANSWER
9.55
EDDIE SAYS
13.5cos45°
  • Question 8

Triangle DEF has a right angle at E.

 

DE = 13.5 cm

 

∠EDF = 54º

 

After sketching the triangle, use trigonometry to calculate the length of the side EF.

 

(Give your answer to 3 sig. figs. and just write the number)

CORRECT ANSWER
18.6
EDDIE SAYS
13.5tan54°
  • Question 9

Triangle DEF has a right angle at E.

 

DE = 13.5 cm

 

∠EFD = 54º

 

After sketching the triangle, use trigonometry to calculate the length of the side EF.

 

(Give your answer to 3 sig. figs. and just write the number)

CORRECT ANSWER
9.81
EDDIE SAYS
13.5/tan54°
  • Question 10

Triangle DEF has a right angle at E.

 

FE = 6.95cm

 

∠EFD = 25.8º

 

After sketching the triangle, use trigonometry to calculate the length of the side DF.

 

(Give your answer to 3 sig. figs. and just write the number)

CORRECT ANSWER
7.72
EDDIE SAYS
6.95/cos25.8°
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