A taut telephone wire extends from the top of a 7-meter tall telephone pole to a stake in the ground 3 meters away. A bug crawled from the stake in the ground up the wire to the top of the telephone pole. Then the bug crawled down to the bottom of the pole and back to the stake. How far did the bug crawl? If necessary, round to the nearest tenth.


To find out how far the bug crawled, we need to calculate the distance the bug traveled in each segment of its journey:

1. **From the stake to the top of the telephone pole along the wire:**
   - This forms a right triangle, with the telephone pole height (7 meters) as one leg and the horizontal distance from the pole to the stake (3 meters) as the other leg. 
   - The length of the wire (the hypotenuse) can be found using the Pythagorean theorem.

\[
\text{Wire length} = \sqrt{(7^2) + (3^2)} = \sqrt{49 + 9} = \sqrt{58} \approx 7.6 \, \text{meters}
\]

2. **From the top of the telephone pole to the bottom of the pole:**
   - The distance here is just the height of the telephone pole, which is 7 meters.

3. **From the bottom of the pole back to the stake:**
   - This is the same distance as the horizontal distance from the pole to the stake, which is 3 meters.

**Total distance crawled by the bug:**

\[
\text{Total distance} = 7.6 \, \text{meters} + 7 \, \text{meters} + 3 \, \text{meters} = 17.6 \, \text{meters}
\]

So, the bug crawled a total distance of **17.6 meters**.

Would you like more details or have any questions?

Here are some related questions to consider:
1. How would the total distance change if the horizontal distance to the stake was doubled?
2. What if the telephone pole was 10 meters tall instead of 7 meters?
3. How does the shape of the wire affect the total distance crawled?
4. Can the bug's journey be broken down into other segments for easier calculation?
5. How would the total distance change if the wire sagged slightly instead of being taut?

**Tip:** Always make sure to account for all segments of a journey in problems like these to ensure the total distance is correct.

Discover how far a bug crawled from the stake to the top of a 7-meter tall telephone pole, then down to the bottom and back to the stake. Includes step-by-step calculation using the Pythagorean theorem. Suitable for students in Grades 7-9.

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