2.28: Cosine rule with surds and area

0606/23/O/N/16 — Question 5 · 7 marks

All lengths are in centimetres.

2.28 diagram
In triangle ABCABC, AC=3+1AC = \sqrt{3} + 1, BC=3−1BC = \sqrt{3} - 1 and ∠ACB=60°\angle ACB = 60^{\degree}.
(i)
Without using a calculator, show that the length of AB=6AB = \sqrt{6}.
[3]
(ii)
Show that ∠CAB=15°\angle CAB = 15^{\degree}.
[2]
(iii)
Without using a calculator, find the area of triangle ABCABC.
[2]