Question

A telegraph post is bent at a point above the ground due to storm. Its top just meets the ground at a distance of $8\sqrt{3}$ metres from its foot and makes an angle of ${30}^0$, then the height of the post is :

• A. 16 metres
• B. 23 metres
• C. 24 metres
• D. 10 metres

Answer 1

Answer: (C)

24 metres

Let $AB$ be the pole and $C$ is the point where it bent.

In $△BCD$

$\tan {30}^o=\frac{BC}{BD}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{BC}{8\sqrt{3}}$

$\Rightarrow BC=\frac{1}{\sqrt{3}}\times 8\sqrt{3}=8m$

Again,

$\sin {30}^o=\frac{BC}{CD}$

$\Rightarrow \frac{1}{2}=\frac{8}{CD}$

$\Rightarrow CD=16m$

$\therefore AB=BC+CD$

$=8+16$

$=24m$

Hence height of the pole is $24$ meters.