$10.5''$ and $32''$ hypotenuse, $a=8.5$, $b=42.5$, what angles are the $10.5''$ and $32''$ Hypotenuse?

Question

I have a ramp that has a concave "kink" in the angle.

The first length of the hypotenuse is $10.5''$, the next is $32''$.

The triangle is $8.5''$ tall ($a$)
The triangle is $42.5''$ long ($b$)

How do I figure out what the angles of the two hypotenuse are?

Answer 1

The Pythagorean theorem tells you that were there no kink, the hypothenuse would be $\sqrt{42.5^2+8.5^2}=43.3417\ldots$ Now you have a triangle whose sides are 43.3417, 10.5 and 32, which is pretty weird since there is no non-degenerate triangle with these sides.