Question

destiny is about to ride a straight water slide. the length of the water slide itself is 15 meters. the splash pool at the end of the slide is 9 meters away from the base of the tower that leads up to the launching platform. how high is the launching platform? meters

Explanation:

Step1: Recognize right - triangle

The water - slide forms the hypotenuse of a right - triangle, the distance from the base of the tower to the splash pool is one leg, and the height of the launching platform is the other leg. Let the height of the launching platform be $h$, the length of the slide $c = 15$ meters, and the base distance $a = 9$ meters. According to the Pythagorean theorem $a^{2}+h^{2}=c^{2}$.

Step2: Rearrange the formula

We can rewrite the Pythagorean theorem to solve for $h$: $h=\sqrt{c^{2}-a^{2}}$.

Step3: Substitute values

Substitute $c = 15$ and $a = 9$ into the formula: $h=\sqrt{15^{2}-9^{2}}=\sqrt{(15 + 9)(15 - 9)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). First, calculate $15+9 = 24$ and $15 - 9=6$. Then $h=\sqrt{24\times6}=\sqrt{144}$.

Step4: Calculate the square root

$\sqrt{144}=12$.

Answer:

12