Finding the angles in a right trapezoid

$\begingroup$

It's been a while since I took Geometry, apologies if this is obvious but I couldn't find an answer while searching. I have a right trapezoid:

Right Trapezoid

The sides a, b, and c are known. Can I find the remaining two angles given the information I have?

$\endgroup$

2 Answers

$\begingroup$

from pedal triangle angle = $\pi/2+\arctan{\frac{c-b}{a}}$

Sorry for my bad English

$\endgroup$ $\begingroup$

enter image description here

You can use also law of cosine:

$${\left(\sqrt{a^2+c^2}\right)}^2=b^2+{\left(\sqrt{a^2+(c-b)^2}\right)}^2-2b\sqrt{a^2+(c-b)^2} \cos \alpha$$

$\endgroup$