Answer:
- B ≈ 64.9°
- C ≈ 45.1°
- c ≈ 82.2
Step-by-step explanation:
The Law of Sines is helpful when you know one side and its opposite angle.
a/sin(A) = b/sin(B) = c/sin(C)
Rearranging gives you ...
B = arcsin(b/a·sin(A)) = arcsin(105/109·sin(70°)) ≈ 64.85138°
C = 180° -B -A = 45.14862°
c = a·sin(C)/sin(A) ≈ 82.23360
_____
Comment on the solution method
You can use the Law of Cosines if you like. The formulation would be ...
a² = b² + c² -2bc·cos(A) . . . . where a, b, and A are known
This gives a quadratic in c, the positive solution being the answer you're looking for. Then, either the law of sines or the law of cosines can be used to find one of the other two angles.
c = 105·cos[70°] + √[856 + 11025·cos[70°]²]
c ≈ 82.2336
