Question

You start driving west for 3 miles, turn right, and drive north for another 11 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 your starting point after driving the given path, you can use the Pythagorean theorem.

1. **Driving West:** You drive 3 miles west.
2. **Turning Right (North):** After that, you turn right and drive 11 miles north.

You have now formed a right triangle where:
- The horizontal leg (west) measures 3 miles.
- The vertical leg (north) measures 11 miles.

To find the straight-line distance from your starting point (the hypotenuse of the triangle), you can use the Pythagorean theorem:

\[
c = \sqrt{a^2 + b^2}
\]

where \( a \) is one leg (3 miles), \( b \) is the other leg (11 miles), and \( c \) is the hypotenuse (the distance from the starting point).

Plugging in the values:

\[
c = \sqrt{3^2 + 11^2}
\]
\[
c = \sqrt{9 + 121}
\]
\[
c = \sqrt{130}
\]
\[
c \approx 11.4 \text{ miles} \text{ (rounded to the nearest tenth)}
\]

Thus, the straight-line distance from your starting point is approximately \( \boxed{11.4} \) miles.