The angle of elevation of the Moon when the length of the shadow of a pole is equal to its height, is

Options

A. `60^(@)`
B. `45^(@)`
C. `90^(@)`
D. `30^(@)`

Answer

To solve the problem of finding the angle of elevation of the Moon when the length of the shadow of a pole is equal to its height, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We have a pole of height \( h \) and the length of its shadow is also \( h \). We need to find the angle of elevation \( \theta \) of the Moon from the tip of the shadow.

2. **Draw a Diagram**:
- Draw a vertical line representing the pole of height \( h \).
- Draw a horizontal line from the base of the pole to the tip of the shadow, which is also of length \( h \).
- The angle of elevation \( \theta \) is formed between the line of sight to the Moon and the horizontal line.

3. **Identify the Right Triangle**:
- The height of the pole is the opposite side of the triangle, which is \( h \).
- The length of the shadow is the adjacent side of the triangle, which is also \( h \).

4. **Use the Tangent Function**:
- The tangent of the angle \( \theta \) is given by the formula:
\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{h}{h} = 1 \]

5. **Find the Angle**:
- We know that \( \tan(\theta) = 1 \). The angle \( \theta \) for which the tangent is 1 is:
\[ \theta = 45^\circ \]

6. **Conclusion**:
- Therefore, the angle of elevation of the Moon when the length of the shadow of the pole is equal to its height is \( 45^\circ \).

### Final Answer:
The angle of elevation of the Moon is \( 45^\circ \).

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