Question

question 10 of 10
what is the length of leg s of the triangle below?
a. 1
b. 4
c. 5√2
d. 2
e. 5.6
f. 4.4

Explanation:

Step1: Identify Triangle Type

The triangle has angles \(90^\circ\), \(45^\circ\), \(45^\circ\), so it's a 45 - 45 - 90 triangle. In such a 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 \(h = 4\sqrt{2}\), use the formula \(h = s\sqrt{2}\). Substitute \(h\):
\(4\sqrt{2}=s\sqrt{2}\)
Divide both sides by \(\sqrt{2}\):
\(s=\frac{4\sqrt{2}}{\sqrt{2}} = 4\).

Answer:

B. 4