Question

How do you determine the number of possible solutions using the rule of law of sines given b = 4, c = 3, Beta = 40 degrees?

Answer 1

Solve triangle knowing b = 4, c = 3, and B = 40 deg
Ans: C = 28.82 deg

Explanation:

Use the trig identity: `sin C/c = sin A/a`

`sin c = (csin B)/b = (3sin 40)/4 = (3(0.64))/4 = 0.48` --> C = 28.82.

There are 2 possible solutions because there are 2 angles that have the same sine value (0.48): C = 28.82 deg and C = 180 - 28.82 = 151.18 deg. However, this answer is rejected because side c < side b.