let alpha = a
beta = b
gamma = g , for easier typing
Since a+b = π/2 or 90°
a , b and g can be assigned values in many ways
a = 50°, b=40°, and g=10° , then we need tan 50°
a = 70° , b = 20°, and g=50°, then we need tan 70°
So tan a cannot be uniquely determined , and I think the question is bogus.
Check your typing.