Question

You start driving west for 5 miles, turn left, and drive south for another 8 miles. At the end of driving, what is your straight line distance from your starting point? Round to the nearest tenth of a mile.

Answer 1

To find the straight-line distance from the starting point after driving west and then south, we can visualize this situation as a right triangle.

1. You start at point A and drive 5 miles west to point B.
2. Then, you turn left (which means you head south) and drive 8 miles to point C.

Now, we have:
- The horizontal leg of the triangle (AB) is 5 miles (west).
- The vertical leg of the triangle (BC) is 8 miles (south).

To find the distance from point A to point C (the straight-line distance), we can use the Pythagorean theorem:

\[
AC = \sqrt{AB^2 + BC^2}
\]

Substituting in the lengths we found:

\[
AC = \sqrt{5^2 + 8^2} = \sqrt{25 + 64} = \sqrt{89}
\]

Calculating \(\sqrt{89}\):

\[
\sqrt{89} \approx 9.433981
\]

Rounding to the nearest tenth of a mile:

\[
AC \approx 9.4 \text{ miles}
\]

Thus, the straight line distance from your starting point is approximately **9.4 miles**.