Answer
B = $48.74^{o}$
C = $21.26^{o}$
c = 48.23
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, C, and c.
Finding B:
We can use the Law of Sines.
$\frac{125}{sin(110^{o})} = \frac{100}{sin(B^{o})}$
Therefore, B = $48.74^{o}$
Finding C:
Since we found 2 other angles, we can use the fact that a triangle has angles that add to $180^{o}$.
180 - 110 - 48.74 = 21.26
Therefore, C = $21.26^{o}$
Finding c:
We can use the Law of Sines.
$\frac{125}{sin(110^{o})} = \frac{c}{sin(21.26^{o})}$
Therefore, c = 48.23
In total:
B = $48.74^{o}$
C = $21.26^{o}$
c = 48.23
