Sine rule and the ambiguous case

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

Question 1Calculator · 2 marks
In triangle $ABC$ , angle $A = 40^\circ$ , angle $B = 65^\circ$ and $BC = 8$ cm.
(a) Work out the length of $AC$ . Give your answer correct to 3 significant figures. (2)
Question 2Calculator · 5 marks
In triangle ABC, angle A is 30 degrees, BC = 8 cm and AC = 12 cm. There are two possible triangles.
(a) Find both possible values of angle B, to 1 decimal place. (3)
(b) Find the larger possible area to 3 significant figures. (2)
Question 3Calculator · 3 marks
(a) In triangle ABC, AB = 12 cm, AC = 9 cm and angle ABC = $35^\circ.$ There are two possible triangles. Work out the larger possible area. Give your answer to 3 significant figures. You must show your working. (3)

Answers and marks

(a) 11.3 cm

(a) 48.6 degrees and 131.4 degrees.

(b) $47.1$ cm²

(a) $53.8$ cm²

P1 Establishing $12\times \sin(35)/9$ or an equivalent valid method.
P1 The two possible angles C are $49.886408...^\circ$ and $130.113591...^\circ.$ Hence angle A is $95.113591...^\circ$ or $14.886408...^\circ.$
A1 Correct answer: $53.8$ cm²

Sine rule and the ambiguous case

Type your working online and see every mark you earned and lost.