0606 P12 - Mar 2020 - Q5 - 7 marks
8077
Do not use a calculator in this question.
The diagram shows the isosceles triangle \(ABC\), where \(AB=AC\) and \(BC=2+4\sqrt3\). The height, \(AD\), of the triangle is \(5-\sqrt3\).
(a) Find the area of the triangle \(ABC\), giving your answer in the form \(a+b\sqrt3\), where \(a\) and \(b\) are integers.
(b) Find \(\tan ABC\), giving your answer in the form \(c+d\sqrt3\), where \(c\) and \(d\) are integers.
(c) Find \(\operatorname{sec}^2 ABC\), giving your answer in the form \(e+f\sqrt3\), where \(e\) and \(f\) are integers.
