Question

The angle of elevation of the top of a $24m$ high pillar from window of a building $6m$ above the ground and the angle of depression of its base are complementary angles. The distance of building from pillar is

• A. $2\sqrt{3}m$
• B. $8\sqrt{3}m$
• C. $12\sqrt{3}m$
• D. $6\sqrt{3}m$

Answer 1

The correct option is D $6\sqrt{3}m$

Let the distance between pillar and building be $x.$

In $△ECD,$

$\tan \left(90-\alpha \right)=\frac{ED}{DC}$

$\Rightarrow \cot \alpha =\frac{6}{x}\dots \left(i\right)$

Now, in $△ABE,$

$\tan \alpha =\frac{AB}{BE}$

$\Rightarrow \tan \alpha =\frac{18}{x}\dots \left(ii\right)$

Multiply equation $\left(i\right)$ and $\left(ii\right),$

$\begin{array}{cc}\tan \alpha \times \cot \alpha & =\frac{18}{x}\times \frac{6}{x}\\ 1& =\frac{108}{x^2}\\ x^2& =108\\ x& =6\sqrt{3}m\end{array}$

Hence, the height of the building is $6\sqrt{3}m.$