Question

the hypotenuse of a 45° - 45° - 90° triangle measures 22√2 units. what is the length of one leg of the triangle? 11 units 22 units 11√2 units 22√2 units

Explanation:

Step1: Recall the properties of a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle

In a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle, the ratio of the sides is \(1:1:\sqrt{2}\), where the legs are of equal length and the hypotenuse \(c\) is related to a leg \(a\) by the formula \(c = a\sqrt{2}\).

Step2: Solve for the leg length \(a\)

Given \(c = 22\sqrt{2}\), from \(c=a\sqrt{2}\), we substitute \(c\) and solve for \(a\).

$$
LATEXBLOCK0
$$

Answer:

22 units