Question

When a plane mirror is placed horizontally on level ground at a distance of $60m$ from the foot of a tower, the ray coming from the top of the tower and its reflected ray from the mirror subtends an angle of 90${}^{\circ }$. What is the height of the tower?

• A. $30m$
• B. $60m$
• C. $90m$
• D. $120$

Answer 1

The correct option is B $60m$

Since the top of the tower and its image in the mirror subtends at the eye makes an angle of ${90}^o$, the other two angles at the beam and mirror interface will be ${45}^o$ each.
Hence we have

$tan{45}^o=\frac{XY}{OY}$

$⟹1=\frac{XY}{60}$

$⟹XY=60m$