Two posts are 25 m and 15 m high and the line joining their tips makes an angle of `45^(@)` with horizontal. The distance between these posts is :

Options

A. 5 m
B. `10//sqrt2m`
C. 10 m
D. `10sqrt2m`

Answer

To solve the problem, we need to find the distance between the two posts given their heights and the angle formed by the line joining their tips with the horizontal. Let's break down the solution step by step.

### Step-by-Step Solution:

1. **Identify the heights of the posts**:
- Let the height of post A (25 m) be represented as AC = 25 m.
- Let the height of post B (15 m) be represented as ED = 15 m.

2. **Determine the height difference between the two posts**:
- The height difference (AB) can be calculated as:
\[ AB = AC - ED = 25 \, \text{m} - 15 \, \text{m} = 10 \, \text{m} \]

3. **Understand the triangle formed**:
- We have a right triangle ABE, where:
- AB = 10 m (the height difference)
- Angle ABE = 45° (the angle with the horizontal)

4. **Use the tangent function**:
- In triangle ABE, we can use the tangent of angle ABE:
\[ \tan(45^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{AB}{BE} \]
- Since \(\tan(45^\circ) = 1\), we have:
\[ 1 = \frac{10 \, \text{m}}{BE} \]

5. **Solve for BE**:
- Rearranging the equation gives:
\[ BE = \frac{10 \, \text{m}}{1} = 10 \, \text{m} \]

6. **Conclusion**:
- The distance between the two posts (BE) is 10 meters.

### Final Answer:
The distance between the two posts is **10 meters**.