1.12: Isosceles triangle area and tangent

0606/13/M/J/17 — Question 4 · 5 marks

In this question, all dimensions are in centimetres.

The diagram shows an isosceles triangle

ABC

, where

AB = AC

. The point

M

is the mid-point of

BC

. Given that

AM = 3 + 2\sqrt{5}

and

BC = 4 + 6\sqrt{5}

, find, without using a calculator,

(i)

the area of triangle

ABC

[2]

(ii)

\tan \angle ABC

, giving your answer in the form

\dfrac{a + b\sqrt{5}}{c}

where

a

b

and

c

are positive integers.

[3]