Question

The angles of elevation of the top of a tower at the top and the foot of a pole of height $10$ m are $30$ ${}^{\circ }$ and $60$ ${}^{\circ }$ respectively. The height of the tower is

• A. $10$ m
• B. $15$ m
• C. $20$ m
• D. None of these

Answer 1

The correct option is B $15$ m

Let AB and CD be the pole and tower respectively.

Let $CD=h$

Then $\angle DAC={60}^{\circ }and\angle DBE={30}^{\circ }$

Now $\frac{CD}{CA}=\tan {60}^{\circ }=\sqrt{3}$

$\therefore CD=\sqrt{3}CA\Rightarrow \frac{h}{\sqrt{3}}=CA$

Again $\frac{DE}{BE}=\tan {30}^{\circ }=\frac{h}{\sqrt{3}}$

$\therefore (h-10)=\frac{BE}{\sqrt{3}}=\frac{CA}{\sqrt{3}}$ ...$[\because BE=CA]$

$=\frac{h/\sqrt{3}}{\sqrt{3}}=\frac{h}{3}\Rightarrow 3h-30=h\Rightarrow 2h=30\Rightarrow h=15$

Hence, height of the power $=15$ m