Two poles of height 13 feet and 25 feet are standing at two ends of a 35 feet wide street. Find the distance between their tops.

Answer

To find the distance between the tops of two poles of heights 13 feet and 25 feet that are standing at two ends of a 35 feet wide street, we can follow these steps:

### Step-by-Step Solution:

1. **Draw a Diagram**:
- Represent the two poles as points A and B.
- Let point C be the top of the 13 feet pole (point A) and point D be the top of the 25 feet pole (point B).
- The distance between the bases of the poles (points A and B) is 35 feet.

2. **Identify the Heights**:
- The height of pole A (point C) is 13 feet.
- The height of pole B (point D) is 25 feet.

3. **Calculate the Vertical Distance**:
- The vertical distance between the tops of the two poles can be calculated as:
\[ \text{Vertical Distance} = \text{Height of pole B} - \text{Height of pole A} = 25 \text{ feet} - 13 \text{ feet} = 12 \text{ feet} \]

4. **Apply the Pythagorean Theorem**:
- We can visualize the situation as a right triangle where:
- One leg (vertical distance) is 12 feet (the difference in height).
- The other leg (horizontal distance) is 35 feet (the width of the street).
- The hypotenuse (distance between the tops of the poles) is what we need to find.
- According to the Pythagorean theorem:
\[ EA^2 = AB^2 + EB^2 \]
where \(EA\) is the distance between the tops of the poles, \(AB\) is the vertical distance (12 feet), and \(EB\) is the horizontal distance (35 feet).

5. **Calculate the Squares**:
- Calculate \(AB^2\) and \(EB^2\):
\[ AB^2 = 12^2 = 144 \]
\[ EB^2 = 35^2 = 1225 \]

6. **Add the Squares**:
- Now add these values:
\[ EA^2 = 144 + 1225 = 1369 \]

7. **Find the Length of EA**:
- Take the square root to find \(EA\):
\[ EA = \sqrt{1369} = 37 \text{ feet} \]

### Conclusion:
The distance between the tops of the two poles is **37 feet**.