Question

find a. 5 2 5\sqrt{2} \sqrt{2}

Explanation:

Step1: Identify the triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the legs are equal, and the hypotenuse \(c\) is related to the leg \(a\) by the formula \(c = a\sqrt{2}\).

Step2: Solve for \(a\)

Given \(c = 5\sqrt{2}\), from \(c=a\sqrt{2}\), we can solve for \(a\) by dividing both sides of the equation by \(\sqrt{2}\). So \(a=\frac{5\sqrt{2}}{\sqrt{2}}\).
Simplifying \(\frac{5\sqrt{2}}{\sqrt{2}}\), the \(\sqrt{2}\) terms cancel out, and we get \(a = 5\).

Answer:

\(5\)