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.
- You start at point A and drive 5 miles west to point B.
- 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.