Question

The $x$ axis, $y$ axis and a line passing through the point $A(6,0)$ form a $△ABC$. If $\angle A=30°$, then the area (in $sq\mathrm{units}$) of the triangle, is

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

Answer 1

The correct option is A

$6\sqrt{3}$

Explanation of the correct option:

Given: In $△ABC$, $\angle A=30°$.

Let's plot the figure,

Thus, $\tan \left(30°\right)=\frac{CB}{6}$

$\Rightarrow$ $\frac{1}{\sqrt{3}}=\frac{CB}{6}$

$\Rightarrow$ $CB=\frac{6\sqrt{3}}{3}$

$\Rightarrow$ $CB=2\sqrt{3}$

Since the area of the triangle is $\frac{1}{2}\times \mathrm{base}\times \mathrm{height}$

Thus, Area $=\frac{1}{2}\times 6\times 2\sqrt{3}$

Area $=6\sqrt{3}$ $\mathrm{Sq}\mathrm{units}$

Hence option $\left(A\right)$ is the correct option.