First, apply the Law of Sines:
[tex] \frac{sinC}{c}= \frac{sinB}{b} [/tex]
And solve for B:
[tex]sinB= \frac{bsinC}{c} [/tex]
[tex]B= sin^{-1}( \frac{bsinC}{c} )[/tex]
B = sin⁻¹(20.2 × sin38 / 18.3)
= sin⁻¹(0.67958)
There are two angles that are a possible solution: 43° and 137° and both can be angles of a triangle (B + C < 180°).
Therefore, the correct answer is D) 43° and 137°.
