I have two RA triangles with a shared common hypotenuse. Given the lengths of the opposite sides of the two right angle triangles, a1 and a2, and the sum of both angles, theta, how can I calculate each angle, theta1 and theta2?
Extend the vertical side of the bottom triangle so that it intersects the upper line. This will form a 3rd triangle with two sides and an angle known. From this you can calculate all remaining angles and sides.
Yes, my statement was incorrect. However one side is known as well as all of the angles. So the solution can still proceed from there.
Using the notation in the attachment (I made this before seeing Skipjack's notation, so I used A, B and C for the angles):
Angles of triangle PQT are A, 90, 90-A.
Therefore, angles of RST are also A, 90, 90-A.
Side RS is known. So all other sides of RST can be determined.
Now, all sides of PQT can be determined.
Triangle sides PS and RS are known, so common hypotenuse PR can be determined.
Angles B and C can now be determined.