GCSE & IGCSE maths practice

Sine rule and area of a triangle questions and answers

The sine rule works in any triangle: $\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$ , where side $a$ is opposite angle $A$ . Use it when you know a side and its opposite angle. For an angle, flip it: $\dfrac{\sin A}{a} = \dfrac{\sin B}{b}$ . The area of any triangle is $\tfrac{1}{2}ab \sin C$ , using two sides and the angle between them.

8 questions · Higher tier · Every answer is checked as you type it, with a full worked solution. Updated 27 Oct 2026.

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Where sine rule and area of a triangle comes up

GCSE (AQA, Edexcel, OCR)	Higher only: know and apply the sine rule to find unknown lengths and angles, and Area = ½ab sin C.
Cambridge IGCSE (0580)	Extended only: use the sine and cosine rules for any triangle, including obtuse angles, and area = ½ab sin C (the formulas are given).

The method

Label sides with lower case, opposite angles with the same capital.
Side: a = b sin A ÷ sin B.
Angle: sin A = a sin B ÷ b, then sin⁻¹.
Area: ½ab sin C with C the angle between a and b.

Sine rule and area of a triangle questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upHigher

In triangle ABC, $A = 40°$ , $B = 60°$ and $a = 8$ cm. Find $b$ , to 3 significant figures.

Question 2Warm-upHigher

In triangle ABC, $A = 35°$ , $C = 75°$ and $c = 12$ cm. Find $a$ , to 3 significant figures.

Exam-style

Question 3Exam-styleHigher

In triangle ABC, $a = 7$ cm, $b = 9$ cm and $A = 40°$ . Angle $B$ is acute. Find $B$ , to 1 decimal place.

Question 4Exam-styleHigher

A triangle has angles $50°$ , $65°$ and $65°$ . The side opposite the $50°$ angle is 10 cm. Find the side opposite a $65°$ angle, to 3 significant figures.

Question 5Exam-styleHigher

Find the area of a triangle with sides 7 cm and 9 cm and an angle of $50°$ between them, to 3 significant figures.

cm²

Question 6Exam-styleHigher

Find the area of a triangle with sides 10 cm and 12 cm and an angle of $30°$ between them.

cm²

Challenge

Question 7ChallengeHigher

In triangle ABC, $a = 12$ cm, $A = 110°$ and $b = 8$ cm. Find $B$ , to 1 decimal place.

Question 8ChallengeHigher

A triangle has sides 8 cm and 12 cm and area 40 cm². The angle between those sides is acute. Find it, to 1 decimal place.

Common mistakes

Pairing a side with an angle that isn't opposite it.
Using the sine rule when you don't know any opposite pair (use the cosine rule).
Using an angle that isn't between the two sides in ½ab sin C.

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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