Question

in a right triangle with the hypotenuse c and the legs a and b, c^2=2ab. find the measure of each acute angle.

Answer 1

We know that, usually,

`c^2 = a^2+b^2`

In this case, we also know that

`c^2 = 2ab`

We deduce that

`a^2+b^2 = 2ab`

If we subtract 2ab from both sides, we get

`a^2-2ab+b^2 = 0 \iff (a-b)^2 = 0 \iff a=b`

So, the triangle is an isosceles right triangle, and so the angles are 90-45-45