Question

you start driving west for 3 miles, turn right, and drive north for another 2 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: Identify the right - triangle

The west - east and north - south directions are perpendicular. The 3 - mile westward drive and 2 - mile northward drive form the two legs of a right - triangle.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 3\) miles and \(b = 2\) miles, and \(c\) is the straight - line distance from the starting point. So \(c=\sqrt{a^{2}+b^{2}}=\sqrt{3^{2}+2^{2}}\).

Step3: Calculate the value of \(c\)

First, calculate \(3^{2}+2^{2}\): \(3^{2}=9\), \(2^{2}=4\), then \(3^{2}+2^{2}=9 + 4=13\). So \(c=\sqrt{13}\approx3.6\) miles.

Answer:

3.6 miles