Suppose that the legs of a right triangle with angles of 45 degrees and 45 degrees both have length y. Fine the length of the hypotenuse.

Question

I don't know how to set up the problem to be able to answer it.

(simplify your answer, including any radicals. Use integer or fractions for any numbers in the expression)

Answer 1

Suppose that the legs of a right triangle with angles of 45 degrees and 45 degrees both have length y. Fine the length of the hypotenuse.

Right angled triangle: θ = 45 degree, x = y

sin θ = Opposite side/Hypotenuse = y/h ==> h = y sin θ = y sin 45 = y(√2/2) ==> h = (√2/2)y

Or

cos θ = Adjacent side/Hypotenuse = x/h ==> h = x cos θ = y cos θ = y cos 45 = y(√2/2) ==> h = (√2/2)y