Question

** this is a 2 - page document!ach variable.23045°xyx = y =

Explanation:

Step1: Identify the triangle type

This is a right - angled isosceles triangle (one angle is \(90^{\circ}\), another is \(45^{\circ}\), so the third angle is also \(45^{\circ}\) as the sum of angles in a triangle is \(180^{\circ}\)). In a right - angled isosceles triangle, the legs are equal (\(x = y\)).

Step2: Apply Pythagorean theorem

By Pythagorean theorem \(x^{2}+y^{2}=30^{2}\). Since \(x = y\), we substitute \(y\) with \(x\). So \(x^{2}+x^{2}=900\), \(2x^{2}=900\), \(x^{2}=450\), \(x=\sqrt{450}=15\sqrt{2}\), and \(y = x=15\sqrt{2}\)

Answer:

\(x = 15\sqrt{2}\), \(y = 15\sqrt{2}\)