To find the straight line distance from your starting point after driving south for 2 miles and then east for 9 miles, we can use the Pythagorean theorem.
You end up at a point that is 2 miles south and 9 miles east of your starting point. This forms a right triangle where:
- One leg (south) = 2 miles
- The other leg (east) = 9 miles
We can denote the distance from the starting point to the end point as \(d\). According to the Pythagorean theorem:
\[ d^2 = (2 \text{ miles})^2 + (9 \text{ miles})^2 \]
Calculating the squares:
\[ d^2 = 4 + 81 \] \[ d^2 = 85 \]
Now, we'll take the square root to find \(d\):
\[ d = \sqrt{85} \approx 9.2195 \]
Rounded to the nearest tenth of a mile, \(d\) is approximately 9.2 miles.
Thus, the straight line distance from your starting point is 9.2 miles.
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