The angle of elevation of the top of a tower at a horizontal distance equal to the height of the tower from the base of the tower is

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. any acute angle

Answer

To solve the problem of finding the angle of elevation of the top of a tower when the horizontal distance from the observer to the base of the tower is equal to the height of the tower, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
- Let the height of the tower be \( h \).
- The horizontal distance from the observer to the base of the tower is also \( h \).

2. **Setting Up the Right Triangle**:
- We can visualize this situation as a right triangle where:
- The height of the tower represents the opposite side of the triangle.
- The horizontal distance from the observer to the base of the tower represents the adjacent side of the triangle.

3. **Using Trigonometric Ratios**:
- The angle of elevation \( \theta \) can be found using the tangent function:
\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{h}{h} = 1 \]

4. **Finding the Angle**:
- To find \( \theta \), we need to determine the angle whose tangent is 1.
- We know that:
\[ \tan(45^\circ) = 1 \]
- Therefore, \( \theta = 45^\circ \).

5. **Conclusion**:
- The angle of elevation of the top of the tower is \( 45^\circ \).