Question

In the diagram $AC=xcm,AB=(x+2)cm$ and angle $A={60}^o$
Find an expression, in term of $x$, for the area of triangle $ABC$.
Given your answer in surd form.

Answer 1

Area$=\frac{1}{2}ab\sin \theta$

$=\frac{1}{2}x(x+2)\sin {60}^o$

$=\frac{1}{2}x(x+2)\frac{\sqrt{3}}{2}$

$=\frac{\sqrt{3}}{4}x(x+2)-\frac{\sqrt{3}}{4}{x}^2+\frac{\sqrt{3}}{2}x$.