GCSE · Pythagoras & right-angled trigonometry

Right-angled trigonometry (SOHCAHTOA)Exam-style questions

Labelling opposite, adjacent and hypotenuse from the angle you are using, choosing the right ratio, finding sides and angles, where the exact values come from, and angles of elevation and depression.

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16 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
Diagram NOT accurately drawn

$PQR$ is a right-angled triangle. $PQ = 9.5$ cm and $QR = 6.2$ cm.

Work out the size of the angle marked $x$ .

Give your answer correct to 1 decimal place. (3 marks)
Level 2 · 3 marksTry it
2
A ladder of length $5$ m leans against a vertical wall. The ladder makes an angle of $70°$ with the horizontal ground.

(a) How far up the wall does the ladder reach? Give your answer correct to 2 decimal places. [2]

(b) How far is the foot of the ladder from the wall? Give your answer correct to 2 decimal places. [2]
Level 2 · 4 marksTry it
3
From a point on level ground $40$ m from the base of a vertical tower, the angle of elevation of the top of the tower is $38°$ .

(a) Work out the height of the tower. Give your answer correct to 3 significant figures. [2]

(b) Work out the distance from the point to the top of the tower. Give your answer correct to 3 significant figures. [2]
Level 2 · 4 marksTry it
4
Here is a right-angled triangle.Diagram NOT accurately drawn

Work out the size of angle $x$ . Give your answer to 1 decimal place.
Level 2 · 2 marksTry it
5
Here is a right-angled triangle.Diagram NOT accurately drawn

Work out the length $y$ .
Level 2 · 2 marksTry it