Question

find z.
image of a right triangle with two 45° angles, one leg labeled ( 4sqrt{6} ) yd, the other leg labeled z
write your answer in simplest radical form.
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Explanation:

Step1: Identify triangle type

The triangle is a right - isosceles triangle (two angles are $45^{\circ}$, one is $90^{\circ}$), so the two legs are equal.

Step2: Determine the value of \(z\)

In a right - isosceles triangle, the legs are of equal length. The given leg length is $4\sqrt{6}$ yd, so \(z = 4\sqrt{6}\) yd.

Answer:

$4\sqrt{6}$