To find the straight-line distance from the starting point after driving, you can use the Pythagorean theorem.
You start by driving 14 miles east and then turn left and drive 6 miles north. This forms a right triangle where:
- One leg (east direction) is 14 miles,
- The other leg (north direction) is 6 miles.
We can find the straight-line distance (hypotenuse \(c\)) from the starting point using the formula:
\[ c = \sqrt{a^2 + b^2} \]
where \(a\) and \(b\) are the two legs of the triangle (the east and north distances). Here, \(a = 14\) miles and \(b = 6\) miles.
Now, plug in the values:
\[ c = \sqrt{14^2 + 6^2} \] \[ = \sqrt{196 + 36} \] \[ = \sqrt{232} \] \[ \approx 15.2 \text{ miles} \]
Thus, the straight-line distance from the starting point to the end point is approximately 15.2 miles when rounded to the nearest tenth.
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