Vì tam giác ABC có góc A = 90°, nên góc B + góc C = 90°.

Gọi góc B = x, góc C = y.

Theo đề bài, góc HAM = 15°, góc HAB = góc HAC = 90° - góc BAC/2 = 90° - (x+y)/2.

Vì góc HAM = 15°, nên góc HMA = 180° - góc HAM = 180° - 15° = 165°.

Vì góc HAB = góc HAC = 90° - (x+y)/2, nên góc HMA = góc HAB + góc BAM = góc HAC + góc CAM.

Do đó, 165° = (90° - (x+y)/2) + (x/2) + (y/2).

Simplifying the equation, we get:

165° = 90° - (x+y)/2 + x/2 + y/2.

165° = 90° + x/2 + y/2 - (x+y)/2.

165° = 90° + (x+y)/2 - (x+y)/2.

165° = 90°.

This equation is not true, so there is no solution for the angles B and C.