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... 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. Read more

Steps to Solve

1. Visualize the problem Imagine a right triangle where the distance traveled west is one leg, the distance traveled north is the other leg, and the straight-line distance from the starting point is the hypotenuse.

2. Apply the Pythagorean theorem The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse ($c$) is equal to the sum of the squares of the lengths of the other two sides ($a$ and $b$). In this case, $a = 3$ miles and $b = 11$ miles. $$ c^2 = a^2 + b^2 $$

3. Calculate the square of the hypotenuse Substitute the given values into the Pythagorean theorem: $$ c^2 = 3^2 + 11^2 = 9 + 121 = 130 $$

4. Solve for the hypotenuse Take the square root of both sides to find $c$: $$ c = \sqrt{130} $$

5. Approximate the square root $$ c \approx 11.40175 $$

6. Round to the nearest tenth Round the result to the nearest tenth of a mile: $$ c \approx 11.4 \text{ miles} $$