Question

gordon bicycles 8 miles west to get from his house to school. after school, he bicycles 4 miles north to his friend spencers house. how far is gordons house from spencers house, measured in a straight line? if necessary, round to the nearest tenth. miles

Explanation:

Step1: Determine the right - angled triangle sides

Gordon's path forms a right - angled triangle. The two legs of the right - angled triangle are \(a = 8\) miles (west - east direction) and \(b=4\) miles (north - south direction). We need to find the length of the hypotenuse \(c\) (the straight - line distance from Gordon's house to Spencer's house) using the Pythagorean theorem \(c^{2}=a^{2}+b^{2}\).

Step2: Substitute the values into the Pythagorean theorem

Substitute \(a = 8\) and \(b = 4\) into the formula \(c^{2}=a^{2}+b^{2}\). So \(c^{2}=8^{2}+4^{2}\).
First, calculate \(8^{2}=64\) and \(4^{2}=16\). Then \(c^{2}=64 + 16=80\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{80}\). We can simplify \(\sqrt{80}=\sqrt{16\times5}=4\sqrt{5}\approx4\times2.236 = 8.944\)

Answer:

\(8.9\) miles