HELP PLEASE! I NEEDED IT! T0T Applying the 45-45-90 Theorem, Find the lengths of the other two sides of a right triangle if the length of the hypotenuse is 4√2 inches and one of the angles is 45°.​

When given the length of the hypotenuse of a 45°-45°-90° triangle, you can calculate the side lengths by simply dividing the hypotenuse by √2.

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Rule: If x is the leg of a 45-45-90 triangle, then x*sqrt(2) is the hypotenuse.

We can prove this by showing that x^2+x^2 = (x*sqrt(2))^2 is an identity. It's from the pythagorean theorem a^2+b^2 = c^2.

Put another way, if we know that a = x and b = x are the two congruent legs, then x^2+x^2 = c^2 leads to c = x*sqrt(2). This triangle is known as an isosceles right triangle.

So if 4*sqrt(2) is the hypotenuse, we match that up with the template x*sqrt(2) and see that x = 4 must be the case.

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