Cosine rule for sides and angles

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Calculator · 3 marks
In triangle $ABC$ , $AC = 7$ cm, $AB = 9$ cm and angle $BAC = 52^\circ$ .
(a) Work out the length of $BC$ . Give your answer correct to 3 significant figures. (3)
Question 2Calculator · 4 marks
A triangle has sides 10 cm, 12 cm and 15 cm.
(a) Find its largest angle to 1 decimal place. (2)
(b) Find its area to 3 significant figures. (2)
Question 3Calculator · 3 marks
(a) From harbour A, boat B is 12 km away on a bearing of $060^\circ$ and boat C is 9 km away on a bearing of $140^\circ.$ Work out the bearing of C from B. Give your answer as a three-figure bearing to the nearest degree. You must show your working. (3)

Answers and marks

(a) 7.24 cm

(a) $85.5$ °

(b) $59.8$ cm²

(a) $200$ °

P1 Establishing $9\times \sin(140)-12\times \sin(60)$ or an equivalent valid method.
P1 Establishing $9\times \cos(140)-12\times \cos(60)$ or an equivalent valid method.
A1 Correct answer: $200$ °

Cosine rule for sides and angles

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