Question

The $x-$ axis, $y-$ axis and a line passing through the point A (6, 0) form a triangle $ABC$. If $\angle A=30{}^\circ ,$ then the area of the triangle, in sunits is

• A. $6\sqrt{3}$
• B. $12\sqrt{3}$
• C. $4\sqrt{3}$
• D. $8\sqrt{3}$

Answer 1

Answer: (A)

$6\sqrt{3}$

Answer 2

In $\Delta AOB,tan\,30{}^\circ =\frac{OB}{OA}$ $\Rightarrow$ $\frac{1}{\sqrt{3}}=\frac{OB}{6}$ $\Rightarrow$ $OB=\frac{6\sqrt{3}}{3}=2\sqrt{3}$ $\therefore$ Area of $\Delta AOB=\frac{1}{2}\times OA\times OB$ $=\frac{1}{2}\times 6\times 2\sqrt{3}=6\sqrt{3}$ sq unit