Question

determine the unknown side lengths.
12 m
45(^{circ})
(x=)
(y=)

Explanation:

Step1: Identify triangle type

This is a right - isosceles triangle (one angle 90°, one angle 45°, so the third angle is 45°). In a right - isosceles triangle, the two legs are equal. So \(x = 12\space m\) (since the leg with length 12 m and the leg with length \(x\) are both legs of the right - isosceles triangle).

Step2: Calculate hypotenuse \(y\)

For a right - isosceles triangle, the hypotenuse \(y\) is related to the leg length \(a\) (here \(a = 12\space m\)) by the formula \(y=a\sqrt{2}\). Substituting \(a = 12\), we get \(y = 12\sqrt{2}\space m\approx16.97\space m\) (or keep it as \(12\sqrt{2}\space m\)).

Answer:

\(x = 12\space m\), \(y = 12\sqrt{2}\space m\) (or approximately \(16.97\space m\))