Question

on the school playground, the slide is 8.5 meters due west of the tire swing and 3.8 meters due south of the monkey bars. what is the distance between the tire swing and the monkey bars? if necessary, round to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the distance between the tire - swing and the slide be $a = 8.5$ meters and the distance between the slide and the monkey - bars be $b = 3.8$ meters. The distance $d$ between the tire - swing and the monkey - bars is the hypotenuse of a right - triangle. According to the Pythagorean theorem $d=\sqrt{a^{2}+b^{2}}$.

Step2: Substitute values

Substitute $a = 8.5$ and $b = 3.8$ into the formula: $d=\sqrt{8.5^{2}+3.8^{2}}=\sqrt{72.25 + 14.44}=\sqrt{86.69}$.

Step3: Calculate the square - root

$\sqrt{86.69}\approx9.3$ (rounded to the nearest tenth).

Answer:

$9.3$