Contributed by:

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles

1.
Name:

Exam Style Questions

Trigonometry

Equipment needed: Calculator, pen

1. Read each question carefully before you begin answering it.

2. Check your answers seem right.

3. Always show your workings

Video Tutorial

www.corbettmaths.com/contents

Videos 329, 330, 331

Answers and Video Solutions

© Corbettmaths 2022

Exam Style Questions

Trigonometry

Equipment needed: Calculator, pen

1. Read each question carefully before you begin answering it.

2. Check your answers seem right.

3. Always show your workings

Video Tutorial

www.corbettmaths.com/contents

Videos 329, 330, 331

Answers and Video Solutions

© Corbettmaths 2022

2.
1. Shown below is a right-angled triangle.

Use trigonometry to work out the size of angle x.

....................°

(3)

Work out the size of angle x

....................°

(3)

© Corbettmaths 2022

Use trigonometry to work out the size of angle x.

....................°

(3)

Work out the size of angle x

....................°

(3)

© Corbettmaths 2022

3.
3. ABC is a right-angled triangle

Work out the size of the angle marked x.

....................°

(3)

4. Below is a right-angled triangle.

Use trigonometry to work out the length x.

....................cm

(3)

© Corbettmaths 2022

Work out the size of the angle marked x.

....................°

(3)

4. Below is a right-angled triangle.

Use trigonometry to work out the length x.

....................cm

(3)

© Corbettmaths 2022

4.
Work out the length x.

....................cm

(3)

Work out the length of RT.

....................cm

(3)

© Corbettmaths 2022

....................cm

(3)

Work out the length of RT.

....................cm

(3)

© Corbettmaths 2022

5.
7. Triangle ABC has a right angle.

Angle BAC is 25°

AC = 12.5cm

Calculate the length of AB

....................cm

(3)

8. DEF is a right-angled triangle.

Calculate the size of angle DEF.

....................°

(3)

© Corbettmaths 2022

Angle BAC is 25°

AC = 12.5cm

Calculate the length of AB

....................cm

(3)

8. DEF is a right-angled triangle.

Calculate the size of angle DEF.

....................°

(3)

© Corbettmaths 2022

6.
Work out the length of side x.

Include suitable units.

....................

(3)

10. Shown is a right-angled triangle

sin30∘ = 0.5

Work out the value of x

....................

(3)

© Corbettmaths 2022

Include suitable units.

....................

(3)

10. Shown is a right-angled triangle

sin30∘ = 0.5

Work out the value of x

....................

(3)

© Corbettmaths 2022

7.
11. A ladder is placed against a vertical wall.

To be safe, it must be inclined at between 70° and 80° to the ground.

(a) Is the ladder safe?

.........................

(3)

(b) Calculate the length of the ladder.

.........................m

(3)

© Corbettmaths 2022

To be safe, it must be inclined at between 70° and 80° to the ground.

(a) Is the ladder safe?

.........................

(3)

(b) Calculate the length of the ladder.

.........................m

(3)

© Corbettmaths 2022

8.
12. A ramp is built to help people enter a building.

The start of the ramp is 2.1 metres from the base of the building.

The ramp has a height of 20 centimetres.

Calculate the size of angle y.

....................°

(3)

13. Shown below is right-angled triangle DEF.

Angle E is 12° larger than angle D

Work out the length of DE.

....................cm

(4)

© Corbettmaths 2022

The start of the ramp is 2.1 metres from the base of the building.

The ramp has a height of 20 centimetres.

Calculate the size of angle y.

....................°

(3)

13. Shown below is right-angled triangle DEF.

Angle E is 12° larger than angle D

Work out the length of DE.

....................cm

(4)

© Corbettmaths 2022

9.
14. The diagram shows two right-angled triangles.

Calculate the value of x.

.........................cm

(5)

© Corbettmaths 2022

Calculate the value of x.

.........................cm

(5)

© Corbettmaths 2022

10.
15. Two right-angled triangles are shown below.

AB is 10cm

BC is 3cm

Angle BCD is 65°

Calculate the size of angle ABD

....................°

(5)

© Corbettmaths 2022

AB is 10cm

BC is 3cm

Angle BCD is 65°

Calculate the size of angle ABD

....................°

(5)

© Corbettmaths 2022

11.
16. The diagram shows a right-angled triangle.

Calculate the length of side x.

.........................cm

(3)

17. ABC is a right-angled triangle.

tan x = 0.6

Work out the length of BC

.........................cm

(3)

© Corbettmaths 2022

Calculate the length of side x.

.........................cm

(3)

17. ABC is a right-angled triangle.

tan x = 0.6

Work out the length of BC

.........................cm

(3)

© Corbettmaths 2022

12.
18. Shown below are right-angled triangles, ABD and BCD.

AB = 15cm

Angle ABD = 70°

Angle ABD : Angle DBC = 5 : 2

Work out the length of CD

.........................cm

(5)

© Corbettmaths 2022

AB = 15cm

Angle ABD = 70°

Angle ABD : Angle DBC = 5 : 2

Work out the length of CD

.........................cm

(5)

© Corbettmaths 2022

13.
19. ABCD is a rectangle.

BD = 9cm

Angle BDC = 40°

(a) Work out the length of BC

.........................cm

(2)

(b) Work out the perimeter of rectangle ABCD

.........................cm

(3)

© Corbettmaths 2022

BD = 9cm

Angle BDC = 40°

(a) Work out the length of BC

.........................cm

(2)

(b) Work out the perimeter of rectangle ABCD

.........................cm

(3)

© Corbettmaths 2022

14.
20. Shown below is a parallelogram.

Calculate the area of the parallelogram.

.........................cm²

(5)

© Corbettmaths 2022

Calculate the area of the parallelogram.

.........................cm²

(5)

© Corbettmaths 2022

15.
21. A regular hexagon can be divided into 6 equilateral triangles.

The diagram below shows one of the equilateral triangles.

(a) Use trigonometry to find the height, x, of the equilateral triangle.

.........................cm

(3)

(b) Calculate the area of the equilateral triangle.

........................cm²

(1)

(c) Calculate the area of the hexagon.

........................cm²

(1)

© Corbettmaths 2022

The diagram below shows one of the equilateral triangles.

(a) Use trigonometry to find the height, x, of the equilateral triangle.

.........................cm

(3)

(b) Calculate the area of the equilateral triangle.

........................cm²

(1)

(c) Calculate the area of the hexagon.

........................cm²

(1)

© Corbettmaths 2022

16.
22. Shown below is isosceles triangle, ABC, where AB = BC

(a) Work out the size of angle BAC

.........................°

(3)

(b) Work out the size of angle ABC

.........................°

(1)

© Corbettmaths 2022

(a) Work out the size of angle BAC

.........................°

(3)

(b) Work out the size of angle ABC

.........................°

(1)

© Corbettmaths 2022

17.
23. Humphrey is flying a kite.

The handle is held 80cm above the ground.

The kite is on a string which is 8m long.

The string makes an angle of 63° with the horizontal.

Calculate the height of the bottom of the kite above the ground.

.........................m

(4)

© Corbettmaths 2022

The handle is held 80cm above the ground.

The kite is on a string which is 8m long.

The string makes an angle of 63° with the horizontal.

Calculate the height of the bottom of the kite above the ground.

.........................m

(4)

© Corbettmaths 2022

18.
24. A helicopter leaves Bristol and flies due east for 10 miles.

Then the helicopter flies 8 miles north before landing.

(a) Work out the direct distance of the helicopter from Bristol.

.................miles

(3)

(b) Calculate the bearing of the helicopter from Bristol.

.........................°

(3)

© Corbettmaths 2022

Then the helicopter flies 8 miles north before landing.

(a) Work out the direct distance of the helicopter from Bristol.

.................miles

(3)

(b) Calculate the bearing of the helicopter from Bristol.

.........................°

(3)

© Corbettmaths 2022

19.
25. A boat is approaching a cliff with a lighthouse on top.

The cliff is 100m high and the lighthouse is 30m tall.

The angle of elevation from the boat to the top of the lighthouse is 20°

(a) Calculate the distance of the boat from the base of the cliff.

.........................m

(3)

(b) Work out the angle of elevation from the boat to the top of the cliff.

.........................°

(3)

© Corbettmaths 2022

The cliff is 100m high and the lighthouse is 30m tall.

The angle of elevation from the boat to the top of the lighthouse is 20°

(a) Calculate the distance of the boat from the base of the cliff.

.........................m

(3)

(b) Work out the angle of elevation from the boat to the top of the cliff.

.........................°

(3)

© Corbettmaths 2022

20.
26. ABCD is a trapezium

Angle BAD = 74°

CD = 19.2cm

AB = 26cm

AM = 2.5cm

Work out the size of angle ABC.

.........................°

(5)

© Corbettmaths 2022

Angle BAD = 74°

CD = 19.2cm

AB = 26cm

AM = 2.5cm

Work out the size of angle ABC.

.........................°

(5)

© Corbettmaths 2022