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.

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

Answer 1

Draw a right triangle ABC with angle A=45° ,angle B=90° and angle C=45° ( rough diagram is enough)

According to pythagoras theorem we have,

AC^2=AB^2 + BC^

Here we are given ,

AB=BC=y

AC^2=Y^2 + Y^2

AC^2=2y^2

Taking square root on both sides we get

AC=(sqrt 2)y       (which is the length of the hypotenuse)