Question

A pole stands vertically on the ground if the angle of elevation at the top of the pole from a point 60 m away from the pole is 30${}^o$, then the height of the pole is:

(Use $\sqrt{3}$ = 1.73)

• A. $34.2m$
• B. $34.3m$
• C. $34.4m$
• D. $34.6m$

Answer 1

The correct option is D $34.6m$

Suppose AB represents the pole,

O is angle of elevation at the top of the pole from a point $60m$ away from the pole.

Then, OA = 60 m, $\angle$O = 30${}^o$

$\therefore tan{30}^o=\frac{AB}{OA}\Rightarrow \frac{1}{\sqrt{3}}=\frac{AB}{60}\Rightarrow AB=\frac{60}{\sqrt{3}}=20\sqrt{3}$.

$\therefore AB=20\times 1.73=34.6m$ $[\sqrt{3}=1.73]$

$\therefore$ Height of the pole is 34.6 m