Question

On the level ground, the angle of elevation of the top of a tower is ${30}^o$. On moving 20 metres nearer to it the angle of elevation becomes ${60}^o$. The height of the tower is :

• A. $10.5m$
• B. $15.2m$
• C. $20m$
• D. $17.32m$

Answer 1

Answer: (D)

$17.32m$

$tan30=\frac{h}{20+x}$
$\frac{1}{\sqrt{3}}=\frac{h}{20+x}$
$h=\frac{20+x}{\sqrt{3}}$
$tan60=\frac{h}{x}$
$h=\sqrt{3}x$
$\sqrt{3}x=\frac{20+x}{\sqrt{3}}$
$3x=20+x,x=10$
$h=\sqrt{3}\times 10$