Question

find s.
3√6 ft
45°
45°
s
write your answer in simplest radical form.
feet

Explanation:

Step1: Identify Triangle Type

The triangle has two \(45^\circ\) angles and a right angle, so it's a 45 - 45 - 90 triangle. In a 45 - 45 - 90 triangle, the legs are equal, and the hypotenuse \(h\) is related to a leg \(s\) by \(h = s\sqrt{2}\).

Step2: Solve for \(s\)

Given hypotenuse \(h = 3\sqrt{6}\), and \(h=s\sqrt{2}\), we solve for \(s\):
\(s=\frac{h}{\sqrt{2}}=\frac{3\sqrt{6}}{\sqrt{2}}\).
Simplify \(\frac{\sqrt{6}}{\sqrt{2}}=\sqrt{\frac{6}{2}}=\sqrt{3}\), so \(s = 3\sqrt{3}\).

Answer:

\(3\sqrt{3}\)