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Grade 5 · Foundation and Higher · free GCSE maths worksheet

Trigonometry: finding a side

SOHCAHTOA in right-angled triangles.

15 original questions, 40 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 ABC, angle ABC = 90° and angle BAC = 34°.

AB = 12 cm.

Work out the length of BC.

Give your answer correct to 3 significant figures.

12 cm34°ABCDiagram NOT accurately drawn
2 marks
Show answer
8.09 cm
2

In triangle PQR, angle PQR = 90° and angle PRQ = 52°.

PQ = 9 cm.

Work out the length of PR.

Give your answer correct to 3 significant figures.

9 cm52°PQRDiagram NOT accurately drawn
2 marks
Show answer
11.4 cm
3

In triangle DEF, angle DEF = 90° and angle EDF = 28°.

DE = 15 cm.

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

2 marks
Show answer
7.98 cm
4

In triangle KLM, angle KLM = 90° and angle LKM = 62°.

KM = 18 cm.

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

2 marks
Show answer
8.45 cm
5

In triangle ABC, angle ABC = 90° and angle ACB = 35°.

AB = 7 cm.

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

2 marks
Show answer
12.2 cm
6

In triangle PQR, angle PQR = 90° and angle QPR = 53°.

QR = 9 cm.

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

2 marks
Show answer
6.78 cm
7

In triangle RST, angle RST = 90° and angle SRT = 41°.

RT = 20 cm.

Calculate the length of RS.

Give your answer correct to 3 significant figures.

20 cm41°RSTDiagram NOT accurately drawn
2 marks
Show answer
15.1 cm
8

A straight ramp is 4.5 m long. It makes an angle of 12° with the horizontal ground.

Work out the horizontal distance the ramp covers. Give your answer correct to 3 significant figures.

2 marks
Show answer
4.40 m
9

A ladder of length 6 m leans against a vertical wall.

The ladder makes an angle of 68° with the horizontal ground.

Work out how far up the wall the ladder reaches.

Give your answer correct to 3 significant figures.

6 m68°ABCWallGroundDiagram NOT accurately drawn
2 marks
Show answer
5.56 m
10

Aisha stands 40 m from the foot of a vertical tower on level ground. The angle of elevation of the top of the tower from her eyes is 36°.

Her eyes are 1.6 m above the ground.

  1. Work out the height of the top of the tower above her eye level. Give your answer correct to 3 significant figures.
  2. Work out the height of the tower above the ground. Give your answer correct to 3 significant figures.
4 marks
Show answer
a) 29.1 m b) 30.7 m
11

tan 40° = (x + 3) ÷ 8

Work out the value of x.

Give your answer correct to 3 significant figures.

3 marks
Show answer
x = 3.71
12

Triangle ABC is isosceles with AB = AC = 10 cm.

Angle BAC = 40°.

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

4 marks
Show answer
6.84 cm
13

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°
14

In triangle ABC, D is the point on AC such that BD is perpendicular to AC.

Angle BAD = 40°, AD = 7 cm and angle BCD = 55°.

Work out the length of BC.

Give your answer correct to 3 significant figures.

7 cm40°55°ADBCDiagram NOT accurately drawn
3 marks
Show answer
7.17 cm
15

In triangle ABC, angle ABC = 90°.

The two acute angles of the triangle are in the ratio 2 : 3.

AC = 15 cm.

Work out the length of the side opposite the larger acute angle.

Give your answer correct to 3 significant figures.

15 cmABCDiagram NOT accurately drawn
4 marks
Show answer
12.1 cm

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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