Answer
C = $15^{o}$
a = 53.54
b = 43.71
Work Step by Step
Note: The Law of Sines is: $\frac{a}{sin(A)}$ = $\frac{b}{sin(B)}$ = $\frac{c}{sin(C)}$
To solve the triangle, we need to find a, b, and C.
Finding C:
Since we are given 2 other angles, we can use the fact that a triangle has angles that add to $180^{o}$.
180 - 120 - 45 = 15
Therefore, C = $15^{o}$
Finding a:
We can use the Law of Sines.
$\frac{a}{sin(120^{o})} = \frac{16}{sin(15^{o})}$
Therefore, a = 53.54
Finding b:
We can use the Law of Sines.
$\frac{b}{sin(45^{o})} = \frac{16}{sin(15^{o})}$
Therefore, b = 43.71
In total:
C = $15^{o}$
a = 53.54
b = 43.71
