Question

a straight waterslide at a theme park is 17 yards long, and it spans a horizontal distance of 8 yards. what is the height at the start of the waterslide?
176.5 yards
between 18 and 19 yards
9 yards
15 yards

Explanation:

Step1: Identify the problem type

This is a right triangle problem where the waterslide is the hypotenuse (\(c = 17\) yards), the horizontal distance is one leg (\(a = 8\) yards), and the height is the other leg (\(b\)) we need to find. We use the Pythagorean theorem: \(a^{2}+b^{2}=c^{2}\).

Step2: Rearrange the formula to solve for \(b\)

From \(a^{2}+b^{2}=c^{2}\), we get \(b^{2}=c^{2}-a^{2}\).

Step3: Substitute the known values

Substitute \(c = 17\) and \(a = 8\) into the formula: \(b^{2}=17^{2}-8^{2}\). Calculate \(17^{2}=289\) and \(8^{2}=64\), so \(b^{2}=289 - 64=225\).

Step4: Solve for \(b\)

Take the square root of both sides: \(b=\sqrt{225}=15\) yards.

Answer:

15 yards