Answer
C = $42.35^{o}$
B = $77.66^{o}$
b = 10.15
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 B, b, and C.
Finding C:
We can use the Law of Sines.
$\frac{9}{sin(60^{o})} = \frac{7}{sin(C^{o})}$
Therefore, C = $42.34^{o}$
Finding B:
Since we know 2 other angles, we can use the fact that a triangle has angles that add to $180^{o}$.
180 - 60 - 42.34 = 77.66
Therefore, B = $77.66^{o}$
Finding b:
We can use the Law of Sines.
$\frac{9}{sin(60^{o})} = \frac{b}{sin(77.66^{o})}$
Therefore, b = 10.15
In total:
C = $42.35^{o}$
B = $77.66^{o}$
b = 10.15
