When a plane mirror is placed horizontally on level ground at a distance of 60 m from the foot of a tower, the top of the tower and its image in the mirror subtend and angle of `90^@` at the eye. The height of the tower is

Options

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

Explanation

To solve the problem, we need to find the height of the tower based on the given information about the angle subtended by the tower and its image in the mirror.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a tower and a plane mirror placed horizontally on the ground.
- The distance from the foot of the tower to the mirror is 60 meters.
- The top of the tower and its image in the mirror subtend an angle of 90 degrees at the observer's eye.

2. **Visualizing the Geometry**:
- Let the height of the tower be \( h \).
- The image of the tower in the mirror will also be at a height \( h \) but located 60 meters away from the mirror (the same height as the tower).
- The observer's eye will be at a point where the line of sight to the top of the tower and the line of sight to the image in the mirror create a right triangle.

3. **Identifying the Angles**:
- Since the angle subtended by the tower and its image is 90 degrees, the angles formed at the observer's eye can be represented as:
- Let \( \theta \) be the angle of elevation to the top of the tower.
- The angle to the image will also be \( \theta \) due to symmetry.
- Therefore, we have \( \theta + \theta = 90^\circ \), which simplifies to \( 2\theta = 90^\circ \), leading to \( \theta = 45^\circ \).

4. **Using Trigonometry**:
- We can use the tangent function to relate the height of the tower and the distance to the mirror:
\[ \tan(45^\circ) = \frac{h}{60} \]
- We know that \( \tan(45^\circ) = 1 \).

5. **Setting Up the Equation**:
- Substituting the value of \( \tan(45^\circ) \) into the equation gives:
\[ 1 = \frac{h}{60} \]

6. **Solving for the Height**:
- Rearranging the equation to find \( h \):
\[ h = 60 \text{ meters} \]

### Conclusion:
The height of the tower is **60 meters**.