Question

A person is standing on the bank of river observer that angle of elevation of the top of the tower standing on the opposite of bank is ${60}^{\circ }$. When he moves $40m$ away from the bank he find the angle of elevation to be ${30}^{\circ }$. Find the height of the tower at width of the river.

• A. $20\sqrt{3}$m
• B. $2\sqrt{3}$m
• C. $5\sqrt{3}$m
• D. None of these

Answer 1

The correct option is A $20\sqrt{3}$m

REF.Image

$tan{60}^{\circ }=\frac{l}{h}$ ___ (i)

$tan{30}^{\circ }=\frac{l-40}{h}$ ___ (ii)

$\frac{\left(i\right)}{\left(ii\right)}$ $3=\frac{l}{l-40}$

$3l-120=l$

$\Rightarrow 2l=120$

$\therefore l=60$

$\frac{\sqrt{3}}{3}=\frac{60-40}{h}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{20}{h}$

$\Rightarrow h=20\sqrt{3}m$

$\therefore$ Height = $20\sqrt{3}$