Question

The angle of elevation of the top of a tower from a distance $100m$ from its foot is ${30}^o$. The height of the tower is:

• A. $100\sqrt{3}m$
• B. $\frac{200}{\sqrt{3}}m$
• C. $50\sqrt{3}m$
• D. $\frac{100}{\sqrt{3}}m$

Answer 1

Answer: (D)

$\frac{100}{\sqrt{3}}m$

Given Angle Of elevation ${30}^{\circ }$

The distance from its foot is $100m$

Consider $\tan$ of the given angle

$⟹\tan \theta =\frac{Height}{Distance}$

$⟹\tan 30=\frac{Height}{100}$

$⟹\frac{1}{\sqrt{3}}=\frac{Height}{100}$

$⟹Height=\frac{100}{\sqrt{3}}$