Question

You start driving east for 14 miles, turn left, and drive north for another 6 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, 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.