GCSE · Trigonometry (sine & cosine rules)

The sine ruleExam-style questions

Why a/sin A = b/sin B holds in any triangle, choosing the sine rule by spotting a matching side–angle pair, turning it upside down to find an angle, and the ambiguous case where two triangles fit.

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

DifficultyAll Level 3 Level 4 Level 5

1
In triangle $ABC$ , angle $A = 52°$ , angle $B = 71°$ and $a = 8.4$ cm.Diagram NOT accurately drawn

Work out the length of $b$ . Give your answer correct to 1 decimal place.
Level 3 · 3 marksTry it
2
In triangle $PQR$ , $p = 12.6$ cm, $q = 9.4$ cm and angle $P = 48°$ .

Angle $Q$ is acute.

Work out the size of angle $Q$ . Give your answer correct to 1 decimal place.
Level 3 · 3 marksTry it
3
In triangle $ABC$ , angle $A = 61°$ , angle $C = 47°$ and $c = 10.5$ cm.

Work out the length of $a$ . Give your answer correct to 3 significant figures.
Level 3 · 3 marksTry it
4
In triangle $PQR$ , $p = 7.8$ cm, angle $P = 42°$ and angle $R = 66°$ .

Work out the length of $r$ . Give your answer correct to 3 significant figures.
Level 3 · 3 marksTry it
5
Diagram NOT accurately drawn

In triangle $PQR$ , $PQ = 8.6$ cm, angle $QPR = 38°$ and angle $PQR = 65°$ .

Work out the length of $QR$ .

Give your answer correct to 3 significant figures. (4 marks)
Level 3 · 4 marksTry it

8 more questions on the sine rule

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