Question

ruth is building a slide for her kids. the ladder is 2 meters tall and the slide is 3 meters long. what is the distance between the ladder and the bottom of the slide? if necessary, round to the nearest tenth. meters

Explanation:

Step1: Identify right - triangle and apply Pythagorean theorem

The ladder, the ground, and the slide form a right - triangle. Let the height of the ladder be $a = 2$ meters, the length of the slide be $c=3$ meters, and the distance between the ladder and the bottom of the slide be $b$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, so $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values and calculate

Substitute $a = 2$ and $c = 3$ into the formula: $b=\sqrt{3^{2}-2^{2}}=\sqrt{9 - 4}=\sqrt{5}\approx2.2$ meters.

Answer:

$2.2$