Question

A tower is 100$\sqrt{3}$ m tall. Find the angle of elevation of its top from a point 100 m away from its foot.

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${45}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

The correct option is B

${60}^{\circ }$

Given:
Height of the tower = $100\sqrt{3}m$
Distance from the tower = $100m$
To find:
Angle of elevation = $\theta$
$\Rightarrow tan\theta =\frac{Oppositeside}{Adjacentside}=\frac{\text{AB}}{\text{BC}}$
​$\Rightarrow tan\theta =\frac{100\sqrt{3}}{100}=\sqrt{3}$
Hence, ​$\therefore \theta ={60}^{\circ }$