Answer
C = $4.52^{o}$
B = $75.48^{o}$
b = 122.87
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 C, B, and b.
Finding C:
We can use the Law of Sines.
$\frac{125}{sin(100^{o})} = \frac{10}{sin(C^{o})}$
Therefore, C = $4.52^{o}$
Finding B:
Since we found 2 other angles, we can use the fact that a triangle has angles that add to $180^{o}$.
180 - 4.52 - 100 = 75.48
Therefore, B = $75.48^{o}$
Finding b:
We can use the Law of Sines.
$\frac{125}{sin(100^{o})} = \frac{b}{sin(75.48^{o})}$
Therefore, b = 122.87
In total:
C = $4.52^{o}$
B = $75.48^{o}$
b = 122.87
