2.21: Exact triangle area and cosine rule

0606/22/O/N/20 — Question 8 · 8 marks

Do not use a calculator in this question. All lengths are in centimetres.

In triangle

ABC

\angle A = 30^{\degree}

AB = 2\sqrt{3} + 1

and the area of the triangle is

5.5\text{ cm}^{2}

(a)

Find the exact length of

AC

. Write your answer in the form

a + b\sqrt{3}

, where

a

and

b

are integers.

[4]

(b)

Show that

BC^{2} = c + d\sqrt{3}

, where

c

and

d

are integers to be found.

[4]