Question

The angle of elevation of the top of a tower at a distance of $300$ metres from its foot on a horizontal plane is found to be ${30}^o$. The height of the tower is

• A. $173m$
• B. $300\sqrt{3}$m
• C. $100m$
• D. None

Answer 1

The correct option is A $173m$

Let the height of the tower is $AB$

Then $\tan {30}^{\circ }=\frac{AB}{AC}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{AB}{300}$

$\Rightarrow AB=\frac{3\times 100}{\sqrt{3}}$

$\Rightarrow AB=\frac{\sqrt{3}\times \sqrt{3}\times 100}{\sqrt{3}}$

$\Rightarrow AB=1.73\times 100=173m$