The problem asks us to find the straight-line distance from the starting point after driving 12 miles east and then 10 miles north. We need to round the answer to the nearest tenth of a mile.

1. Problem Description

The problem asks us to find the straight-line distance from the starting point after driving 12 miles east and then 10 miles north. We need to round the answer to the nearest tenth of a mile.

2. Solution Steps

The problem can be solved using the Pythagorean theorem. The distances traveled east and north form two legs of a right triangle, and the straight-line distance from the starting point is the hypotenuse. Let $a$ be the distance traveled east, $b$ be the distance traveled north, and $c$ be the straight-line distance from the starting point.

We have $a = 12$ miles and $b = 10$ miles. We want to find $c$.

According to the Pythagorean theorem:

$a^2 + b^2 = c^2$

Substituting the given values:

$12^2 + 10^2 = c^2$

$144 + 100 = c^2$

$244 = c^2$

Taking the square root of both sides:

$c = \sqrt{244}$

$c \approx 15.62049935$

Rounding to the nearest tenth of a mile:

$c \approx 15.6$ miles

3. Final Answer

15.6 mi