Calculate leg lengths x and y in a 45-45-90 right triangle with hypotenuse √10

Question

Solve for x and y in a right triangle with two 45° angles, hypotenuse length √10.

Accepted Answer

x=√5, y=√5

Answer

Step 1: Identify the triangle is a 45-45-90 special right triangle, which is an isosceles right triangle, so the two legs are equal. Step 2: Use the property that legs = hypotenuse / √2. Substitute hypotenuse = √10: x = y = √10 / √2 = √5.