Two cars leave the same parking lot, with one heading north and the other heading east. After several minutes, the eastbound car has traveled 4 kilometers. If the two cars are now a straight-line distance of 9 kilometers apart, how far has the northbound car traveled? If necessary, round to the nearest tenth.

This problem involves a right triangle, where the cars' distances from the parking lot form the legs, and their straight-line distance forms the hypotenuse.

Let:
- \( d_N \) be the distance the northbound car has traveled (in kilometers).
- The eastbound car has traveled 4 kilometers.
- The straight-line distance between the cars is 9 kilometers.

By the Pythagorean theorem, we know:
\[
d_N^2 + 4^2 = 9^2
\]
Substitute the values for the distances:
\[
d_N^2 + 16 = 81
\]
Solve for \( d_N^2 \):
\[
d_N^2 = 81 - 16 = 65
\]
Now take the square root of both sides to find \( d_N \):
\[
d_N = \sqrt{65} \approx 8.1 \, \text{kilometers}
\]

Thus, the northbound car has traveled approximately 8.1 kilometers.

Would you like more details or have any questions?

Here are five related questions:
1. What if the straight-line distance was 10 kilometers instead of 9 kilometers?
2. How would the answer change if the eastbound car had traveled 5 kilometers?
3. Can you use the Pythagorean theorem to find distances in three-dimensional space?
4. What is the significance of the Pythagorean theorem in navigation and travel?
5. How would you calculate the time taken by each car if their speeds were known?

**Tip:** The Pythagorean theorem only applies to right triangles, where one angle is exactly 90 degrees.

Learn how to calculate the distance traveled by a northbound car using the Pythagorean Theorem. Given an eastbound car's distance of 4 kilometers and a straight-line distance of 9 kilometers between the cars, this problem covers key geometric concepts, including the application of the Pythagorean Theorem. Suitable for students in Grades 8-10.

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