I've attached a perspective sketch of the folded triangle.
1. You already know:
2. Draw the line . It is the hypotenuse of the isosceles right triangle BMC.
3. Construct the midpoint of BC = M'
4. The length of ist calculated by
5. Since the line segment has the length
6. The angle is the angle between the plane BMC and the plane ABC. It can be calculated by
And therefore the angle