Solve right triangle given two points.

Question

I am trying to solve a right triangle given the coordinated of two points. This diagram explains the triangle better

We know the coordinates of point A and point C, we also know that the angle of b is 90 degrees. I would like to be able to find all the angles and side lengths. I know we can find the length of the hypotenuse using the distance formula the two known points however I am not sure where to go from here.

Thanks!

Answer 1

$B$ can be any point on the circle with diameter $AC$. Therefore neither angles nor side lengths can be determined. In other words the problem has a solution for any $0<\alpha<\frac\pi2$, and for any $0<a<b$.

Answer 2

Unfortunately, this is not enough information to find it. If you draw a circle with diameter $AC$, $B$ could be anywhere on this circle. If we choose it properly, we can have the angles at $A$ and $C$ could be any two angles that sum up to 90 degrees.

Answer 3

A corollary of Euclidian geometry says:

All inscribed angles in a semicircunference are right angles.

Like in this gif

So you have infinite answers to your question