I've been working on these spherical trig questions that I initially thought were rather straightforward. Instead, my attempts to finish this assignment have descended into madness because I cannot--for the life of me--figure out where I'm going wrong.
Problem: I'm given three subtending angles a = 37◦15′, b = 29◦51′, c = 20◦49′, and one interior angle C = 34◦37' of a spherical triangle;
I am asked to find the remaining interior angles A and B using the spherical sine law.
Attempt: I know that the interior angles A + B + C must be greater than/equal to 180 degrees.
From the spherical law of sines: sin(A)/sin(a) = sin(B)/sin(b) = sin(C)/sin(c).
Thus, after converting from DMS to decimal degrees:
sin(A)/sin(37.25◦) = sin(B)/sin(29.85◦) = sin(34.617◦)/sin(20.817◦)
Splitting these into 2 equalities, I solved for A and B and found:
A = 75.371◦ and B = 52.715◦
By observation, A + B + C < 180◦, which is not possible for a spherical triangle.
I have reworked this problem several times, both in radians and degrees, and I can never get it. I am either making a careless error, or deeply misunderstanding spherical trig; either way, I would really appreciate it if someone could clear this up please. Cheers!