Let a = 2 cm, b = 6 cm, and angle A = 60°. How many solutions are there for angle B
We must calculate b sin A. If it is less than a, there will be two solutions. If it is equal to a, there will be one solution. And if it is greater than a, there will be no solution.
Now, sin 60° =
3^{1/2}/ 2
Therefore,
b sin A
= 6·
=
3.3^{1/2}
.
Since a = 2, then b sin A > a. (3^{1/2 = }1.732).
There is no solution.