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.

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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 $ABC$ , $b = 7.5$ cm, $c = 10.2$ cm and angle $A = 118°$ .Diagram NOT accurately drawn

(a) Work out the length of $a$ . Give your answer correct to 1 decimal place.

(b) Explain why $a$ must be longer than $\sqrt{7.5^2 + 10.2^2}$ .
Level 5 · 5 marksTry it
2
Two ships leave a port at the same time. Ship $A$ sails $12$ km on a bearing of $040°$ . Ship $B$ sails $18$ km on a bearing of $115°$ .

Work out the distance between the two ships. Give your answer correct to 3 significant figures.
Level 5 · 4 marksTry it
3
The diagram shows quadrilateral $ABCD$ and its diagonal $AC$ . $AB = 9.4$ cm $\qquad$ angle $ABC = 112°$ $\qquad$ angle $CAD = 41°$ $\qquad$ angle $ACD = 63°$

Triangle $ABC$ has an area of $38$ cm²

Work out the area of triangle $ACD$ .

Give your answer correct to 3 significant figures.

(5 marks)
Level 5 · 5 marksTry it
4
$ABCD$ is a quadrilateral. $AB = 8$ cm $\qquad$ $AD = 11$ cm $\qquad$ $CD = 9.5$ cm

angle $BAD = 72°$ $\qquad$ angle $BCD = 58°$

Find the size of angle $BDC$ .

Give your answer correct to the nearest degree.

(5 marks)
Level 5 · 5 marksTry it