GCSE · Trigonometry (sine & cosine rules)

The cosine ruleExam-style questions

Why a² = b² + c² − 2bc cos A is Pythagoras with a correction term, when to choose it over the sine rule, and the rearrangement that finds an angle from three sides.

Start practising Read the lesson

19 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 $ABC$ , $b = 9$ cm, $c = 13$ cm and angle $A = 67°$ .Diagram NOT accurately drawn

Work out the length of $a$ . Give your answer correct to 1 decimal place.
Level 3 · 3 marksTry it
2
In triangle $ABC$ , $b = 8.2$ cm, $c = 6.5$ cm and angle $A = 54°$ .

Work out the length of $a$ . Give your answer correct to 3 significant figures.
Level 3 · 3 marksTry it
3
A triangle has sides of length $6$ cm, $9$ cm and $11$ cm.

Work out the size of the largest angle of the triangle. Give your answer correct to 1 decimal place.
Level 4 · 3 marksTry it
4
A triangle has sides of length $7$ cm, $8$ cm and $12$ cm.

Work out the size of the smallest angle of the triangle. Give your answer correct to 1 decimal place.
Level 4 · 3 marksTry it
5
A ship sails $40$ km from port $A$ to a buoy $B$ . It then turns and sails $65$ km from $B$ to port $C$ .

Angle $ABC = 105°$ .

Work out the direct distance from $A$ to $C$ . Give your answer correct to 1 decimal place.
Level 4 · 3 marksTry it

14 more questions on the cosine rule

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free