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

30 meters

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60 meters

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90 meters

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120 meters

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Solution

The correct option is B 60 meters
Answer is B.

The angle subtended at the eye by the top of the tower with respect to the ground os 45 degrees. This happens when the height of the tower is equal to tis distance from the eye. The eye is assumed to be very near to the mirror. (Refer below figure).
Angle subtended by AB = 90 degrees/2 = 45 degrees.
Therefore, $t a n θ = \frac{h}{60} . T h a t i s, t a n 45 = \frac{h}{60} . S o, h = 60 m$ .
Hence, the height of the tower is 60 m.

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