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 6 feet and the distance between the tire swing and the monkey bars is 9 feet, how far is the slide from the monkey bars? if necessary, round to the nearest tenth.

Explanation:

Step1: Identify the right - angled triangle

Let the slide be \(S\), the tire swing be \(T\), and the monkey bars be \(M\). Since the slide is due west of the tire swing and due south of the monkey bars, \(\triangle STM\) is a right - angled triangle with \(\angle S = 90^{\circ}\), \(ST = 6\) feet and \(TM=9\) feet. We want to find \(SM\).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that in a right - angled triangle \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the other two sides. In \(\triangle STM\), if we let \(a = ST = 6\), \(c=TM = 9\) and \(b = SM\), then \(SM=\sqrt{TM^{2}-ST^{2}}\) (derived from \(ST^{2}+SM^{2}=TM^{2}\)).
Substitute \(ST = 6\) and \(TM = 9\) into the formula:

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Answer:

\(6.7\)