Question

the length of the shorter leg of the triangle on the inflatable slide is 12 feet. use the $30^{\circ}-60^{\circ}-90^{\circ}$ triangle theorem to determine the length of the hypotenuse and the longer leg of the triangle. enter the answer in the space provided. use numbers instead of words. hypotenuse \boxed{} feet

Explanation:

Step1: Recall 30-60-90 Triangle Theorem

In a \(30^\circ - 60^\circ - 90^\circ\) triangle, the sides are in the ratio \(1 : \sqrt{3} : 2\), where the shorter leg (opposite \(30^\circ\)) is \(x\), the longer leg (opposite \(60^\circ\)) is \(x\sqrt{3}\), and the hypotenuse is \(2x\).

Step2: Identify the shorter leg value

Given the shorter leg \(x = 12\) feet.

Step3: Calculate the hypotenuse

Using the ratio, hypotenuse \(= 2x\). Substitute \(x = 12\): \(2\times12 = 24\).

Answer:

24