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 $A = 43°$ , angle $B = 68°$ and $c = 15.2$ cm.

(a) Work out the size of angle $C$ .

(b) Work out the length of $a$ . Give your answer correct to 1 decimal place.
Level 4 · 4 marksTry it
2
A surveyor stands at point $A$ and sights a mast at point $C$ . She then walks to point $B$ .

In triangle $ABC$ , angle $A = 35°$ , angle $C = 104°$ and $b = 27$ m.

(a) Work out the size of angle $B$ .

(b) Work out the distance $a$ . Give your answer correct to 1 decimal place.
Level 4 · 4 marksTry it
3
In triangle $XYZ$ , $x = 11.2$ cm, $y = 8.6$ cm and angle $X = 74°$ .

Angle $Y$ is acute.

Work out the size of angle $Y$ . Give your answer correct to 1 decimal place.
Level 4 · 3 marksTry it
4
In triangle $ABC$ , $b = 14$ cm, angle $A = 30°$ and angle $B = 110°$ .

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

(b) Work out the length of $c$ . Give your answer correct to 3 significant figures.
Level 4 · 4 marksTry it
5
In triangle $ABC$ , $BC = 9.5$ cm, $AC = 7$ cm and angle $BAC = 68°$ .

Angle $ABC$ is acute.

(a) Work out the size of angle $ABC$ . Give your answer correct to 1 decimal place. (3 marks)

(b) Work out the area of triangle $ABC$ . Give your answer correct to 3 significant figures. (2 marks)
Level 4 · 5 marksTry it