Question

gus and helen went on a hiking trip. they parked their car and started to hike due south, then due east, and so on. after hiking only 216 feet, it started to rain, so they decided to return to the car. this map shows the directions and distances they hiked before it started to rain.

Explanation:

Step1: Identify the right - angled triangles

We can consider the path as composed of right - angled triangles. The horizontal and vertical displacements form the legs of the right - angled triangles.

Step2: Use the Pythagorean theorem

The Pythagorean theorem states that for a right - angled triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c=\sqrt{a^{2}+b^{2}}\).
First, consider the first part of the path. The horizontal displacement \(a_1 = 72\) ft and the vertical displacement \(b_1=72\) ft. The length of the first diagonal part \(d_1=\sqrt{72^{2}+72^{2}}=\sqrt{2\times72^{2}} = 72\sqrt{2}\) ft.
Next, for the second part, the horizontal displacement \(a_2 = 72\) ft and the vertical displacement \(b_2 = 60\) ft. The length of the second diagonal part \(d_2=\sqrt{72^{2}+60^{2}}=\sqrt{5184 + 3600}=\sqrt{8784}= \sqrt{144\times61}=12\sqrt{61}\) ft.
The last part is a straight - line of length \(d_3 = 12\) ft.
The total distance from the starting point to the car is \(d=d_1 + d_2+d_3=72\sqrt{2}+12\sqrt{61}+12\).
\(72\sqrt{2}\approx72\times1.414 = 101.808\), \(12\sqrt{61}\approx12\times7.810=93.72\).
\(d\approx101.808+93.72 + 12=207.528\) ft.

Answer:

Approximately \(207.53\) ft