Question

How do you determine the number of possible solutions using the rule of law of sines given b=15.2, A=12°30', C=57°30'?

Answer 1

Solve triangle knowing b, A, and C

Explanation:

Find B, a and c.
Angle B = 180 - C - A = 180 - 57.30 - 12.30 =`110.40` deg
Use trig identity: `a/sin A = b/sin B`

`a = b(sin B/sin A) = 15.2(0.94/0.21) = 68.04`,

There are 2 possible solutions, because 0.94 is the same sin value of 2 angles: B = 110.40 and B = 69.60. However, the solution angle B = 69.60 is rejected, because the sum A + B + C must be 180 deg.

`c = b(sin B/sin C) = 15.2(0.94/0.84) = 17.00`