Question

harold is building a slide for his kids. the ladder is 2.1 meters tall and the slide is 2.6 meters long. what is the distance between the ladder and the bottom of the slide? if necessary, round to the nearest tenth.

Explanation:

Step1: Identify the right - angled triangle

The ladder, the ground, and the slide form a right - angled triangle. The height of the ladder is one leg ($a = 2.1$ meters), the length of the slide is the hypotenuse ($c = 2.6$ meters), and we need to find the other leg ($b$).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$. We can rewrite it to solve for $b$: $b=\sqrt{c^{2}-a^{2}}$.
Substitute $a = 2.1$ and $c = 2.6$ into the formula:
$b=\sqrt{2.6^{2}-2.1^{2}}=\sqrt{(2.6 + 2.1)(2.6 - 2.1)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$)
$=\sqrt{4.7\times0.5}=\sqrt{2.35}\approx1.5$

Answer:

$1.5$