Question

When a plane mirror is placed horizontally on a level ground at a distance of $60\text{m}$ from the foot of a tower, the top of the tower and its image in the mirror subtend an angle of ${90}^{\circ }$ at O. The height of the tower will be

• A. $30\text{m}$
• B. $60\text{m}$
• C. $90\text{m}$
• D. $120\text{m}$

Answer 1

The correct option is B $60\text{m}$


Let $h$ be the height of the tower.

As tower and its image is subtending an angle of ${90}^{\circ }$.

Therefore, $\theta$ in triangle $\text{AOB}$ is $\theta ={45}^{\circ }$ and Base $\text{OB}=60\text{m}$

$\therefore \frac{h}{60}=\tan {45}^{\circ }\Rightarrow h=60\tan {45}^{\circ }$

$\Rightarrow h=60\text{m}$

Hence, option $\left(b\right)$ is correct.