Robinson Tuition
Grade 5 · Foundation and Higher · free GCSE maths worksheet

Trigonometry: finding an angle

Using inverse sin, cos and tan.

14 original questions, 45 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

In triangle DEF, angle DEF = 90°.

DE = 10 cm and EF = 7 cm.

Work out the size of angle FDE.

Give your answer correct to 1 decimal place.

10 cm7 cmDEFDiagram NOT accurately drawn
2 marks
Show answer
35.0°
2

In a right-angled triangle, the side opposite angle x is 5 cm and the hypotenuse is 8 cm.
Work out the size of angle x. Give your answer correct to 1 decimal place.

2 marks
Show answer
38.7°
3

In a right-angled triangle, the side next to angle y is 6.4 cm and the hypotenuse is 9.2 cm.
Work out the size of angle y. Give your answer correct to 1 decimal place.

2 marks
Show answer
45.9°
4

In triangle JKL, angle JKL = 90°.

JK = 5 cm and JL = 13 cm.

Work out the size of angle KJL.

Give your answer correct to 1 decimal place.

5 cm13 cmJKLDiagram NOT accurately drawn
2 marks
Show answer
67.4°
5

A ladder 5 m long leans against a vertical wall. The foot of the ladder is 1.4 m from the wall on level ground.
Work out the angle the ladder makes with the wall. Give your answer correct to 1 decimal place.

3 marks
Show answer
16.3°
6

Jamal stands 40 m from the base of a vertical tower on level ground. The tower is 18 m high. Ignore Jamal's height.
Work out the angle of elevation of the top of the tower from Jamal. Give your answer correct to 1 decimal place.

3 marks
Show answer
24.2°
7

A straight ramp is 6 m long and rises 0.8 m.
Work out the angle the ramp makes with the horizontal. Give your answer correct to 1 decimal place.

3 marks
Show answer
7.7°
8

Rectangle PQRS has PQ = 12 cm and QR = 5 cm. The diagonal PR is drawn.
Work out the size of angle QPR. Give your answer correct to 1 decimal place.

3 marks
Show answer
22.6°
9

An isosceles triangle has two equal sides of length 10 cm and a base of 12 cm. The perpendicular from the top vertex to the base meets the base at its midpoint.

  1. Work out the size of one base angle. Give your answer to 1 decimal place.
  2. Work out the size of the angle at the top vertex.
4 marks
Show answer
a) 53.1° b) 73.7°
10

A tree is 9 m tall. A second tree next to it is twice as tall. Dev stands on level ground 15 m from the base of the taller tree. Ignore Dev's height.
Work out the angle of elevation of the top of the taller tree from Dev. Give your answer correct to 1 decimal place.

3 marks
Show answer
50.2°
11

The diagram shows triangle ABC with a right angle at B. D is a point on BC. Give each answer correct to 1 decimal place.

  1. Work out the size of angle ADB.
  2. Work out the size of angle ACB.
  3. Work out the size of angle DAC.
ABC6 cm4 cm8 cmDDiagram NOT accurately drawn
5 marks
Show answer
a) 56.3° b) 26.6° c) 29.7°
12

The diagram shows a quadrilateral ABCD split by the diagonal AC. Angle ABC and angle CAD are both right angles. AB = 5 cm, BC = 12 cm and AD = 9 cm.

  1. Work out the length of AC.
  2. Work out the size of angle ADC. Give your answer correct to 1 decimal place.
  3. Work out the size of angle BCD. Give your answer correct to 1 decimal place.
ABCD5 cm12 cm9 cmDiagram NOT accurately drawn
6 marks
Show answer
a) 13 cm b) 55.3° c) 57.3°
13

In triangle ABC, angle ABC = 90°.

AB = 15 cm and BC = 8 cm.

  1. Work out the size of angle BAC. Give your answer correct to 1 decimal place.
  2. Write down the size of angle BCA, correct to 1 decimal place.
15 cm8 cmABCDiagram NOT accurately drawn
3 marks
Show answer
a) 28.1° b) 61.9°
14

In triangle ABC, angle ABC = 90° and angle BAC = 27°. AB = 11 cm.

  1. Work out the length of BC. Give your answer correct to 3 significant figures.

In triangle PQR, angle PQR = 90°. PQ = 9 cm and PR = 14 cm.

  1. Work out the size of angle PRQ. Give your answer correct to 1 decimal place.
11 cm27°ABCDiagram NOT accurately drawn(a)9 cm14 cmPQRDiagram NOT accurately drawn(b)
4 marks
Show answer
a) 5.60 cm b) 40.0°

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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