Question

On the level ground the angle of elevation of the top of a tower is ${30}^{\circ }$ On moving 20 m nearer the angle of elevation is ${60}^{\circ }$. The height of the tower is

• A. $10m$
• B. $15m$
• C. $10\sqrt{3}$ m
• D. $20m$

Answer 1

Answer: (C)

$10\sqrt{3}$ m

Distance between length of shadows = $20$ m when the angle of elevation changes from ${30}^{\circ }$ to ${60}^{\circ }$
Let the length of pole = $p$
Length of shadow when angle of elevation = ${30}^{\circ }$
Shadow =$p\tan 30=\frac{p}{\sqrt{3}}$
Length of shadow when angle of elevation = ${60}^{\circ }$
Shadow =$p\tan 60=p\sqrt{3}$
Distance between the two shadows = $p\sqrt{3}-\frac{p}{\sqrt{3}}$ = $20$
$3p-p=20\sqrt{3}$
$p=10\sqrt{3}$ m