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.