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 $ABC$ , $b = 9.1$ cm, $c = 12.4$ cm and angle $B = 39°$ .

Angle $C$ is obtuse.

Work out the size of angle $C$ . Give your answer correct to 1 decimal place.
Level 5 · 4 marksTry it
2
Two people, $A$ and $B$ , stand on level ground on the same side of a vertical tower, in line with its base. $A$ and $B$ are $50$ m apart, and $B$ is nearer the tower.

From $A$ the angle of elevation of the top of the tower, $T$ , is $32°$ . From $B$ the angle of elevation of $T$ is $55°$ .

(a) Work out the length $BT$ . Give your answer correct to 3 significant figures.

(b) Hence work out the height of the tower. Give your answer correct to 3 significant figures.
Level 5 · 4 marksTry it