Question

you start driving west for 5 miles, turn left, and drive south for another 8 miles. at the end of driving, what is your straight line distance from your starting point? round to the nearest tenth of a mile.

Explanation:

Step1: Recognize the right - triangle

Driving west and then south forms a right - triangle. Let \(a = 5\) miles (westward distance) and \(b=8\) miles (southward distance). The straight - line distance \(c\) from the starting point is the hypotenuse of the right - triangle.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\). Substitute \(a = 5\) and \(b = 8\) into the formula:

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Step3: Calculate the value

\(\sqrt{89}\approx9.4\) (using a calculator, \(\sqrt{89}\approx9.43398\), and rounding to the nearest tenth)

Answer:

\(9.4\) miles