Question

Two poles of equal heights are standing opposite to each other on either side of a road, which is $100$ metres wide. From a point between them on the road, the angles of elevation of their tops are $30$ and $60$. The height of each pole is :

• A. $44$ m
• B. $43.25$ m
• C. $50$ m
• D. $40.5$ m

Answer 1

Answer: (B)

$43.25$ m

Let $AB$ and $CD$ be the two poles and $M$ be the point where the angle of elevation is made of ${30}^0$ and ${60}^0$ respectively.

Let the road $CM$ $=x$ m and $AM$ $=100-x$ m

In right angled $△MCD$, we have

$\tan {60}^0=\frac{DC}{CM}$

$\Rightarrow \sqrt{3}=\frac{h}{x}$

$\Rightarrow h=x\sqrt{3}$ (i)

In right angled $△MAB$, we have

$\Rightarrow \tan {30}^0=\frac{BA}{AM}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{100-x}$

$\Rightarrow h\sqrt{3}=100-x$

$\Rightarrow \left(x\sqrt{3}\right)\sqrt{3}=100-x$ ....(from {i})

$\Rightarrow 3x=100-x$

$\Rightarrow 4x=100$

$\Rightarrow x=25$ m

Therefore, height of pole $CD$,

$\Rightarrow CD=25\times 1.732$

$\Rightarrow CD=43.25$m

Thus, height of each pole is $43.25$ m.