Answer: the sides are a = 7, b = 8, c = 10.
Explanation:
1) Use the law of sines:
sin(A) sin(B)
----------- = --------- =>
a b
2) Solve for B:
sin(B) = b * sin(A) / a = 8 * sin(44°) / 7 = 0.79389528
=> B = arcsin(0.79389528) = 52.55°
3) A + B + C = 180° => C = 180° - A - B = 180° - 44° - 52.55° = 83.45°
4) Use the law of sines again:
sin(A) sin(C)
------------- = -------------
a c
5) Solve for c:
c = sin(C) * a / sin(A) = sin(83.45°) * 7 / sin(44°) = 10.0
Answer: a = 7, b = 8, c = 10.
