Question

on the school playground, the slide is due west of the tire swing and due south of the monkey bars. if the distance between the slide and the tire swing is 7 feet and the distance between the tire swing and the monkey bars is 10 feet, how far is the slide from the monkey bars? if necessary, round to the nearest tenth. feet

Explanation:

Step1: Identify the right - angled triangle

The positions of the slide, tire swing, and monkey bars form a right - angled triangle. Let the distance between the slide and the tire swing be \(a = 7\) feet (one leg of the right - triangle), the distance between the tire swing and the monkey bars be \(c=10\) feet (the hypotenuse of the right - triangle), and the distance between the slide and the monkey bars be \(b\).

Step2: Apply the Pythagorean theorem

According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), we can solve for \(b\). Rearranging the formula gives \(b=\sqrt{c^{2}-a^{2}}\).
Substitute \(a = 7\) and \(c = 10\) into the formula: \(b=\sqrt{10^{2}-7^{2}}=\sqrt{100 - 49}=\sqrt{51}\).

Step3: Calculate the value

\(\sqrt{51}\approx7.1\) (rounded to the nearest tenth)

Answer:

\(7.1\)