question_answer

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 sq unit is

A)  \[6\sqrt{3}\]                     

B)  \[12\sqrt{3}\]

C)  \[4\sqrt{3}\]     

D)         \[8\sqrt{3}\]

E)  \[2\sqrt{3}\]

Correct Answer: A

Solution :

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