Question

How do you determine the number of possible solutions using the rule of law of sines given Angle A=37 degrees, a=49, b=54?

Answer 1

Solve triangle knowing A = 37, a = 49 and b = 54
Ans: 2 solutions,

Explanation:

Find angle B by the Law of Sine: `sin B/b = sin A/a`
`sin B = (b/a)sin A = (54/49)0.60 = 0.66`
Two possible solutions.
sin x = 0.66 --> `x = 41^@55` and `x = 180 - 41.55 = 138^@45`.
These 2 arcs (angles) have the same sin value (0.66).
The right answer is 41^@55. The angle B = 138.45 would require a side b larger than b = 54.