Answer
B = $36.82^{o}$
C = $67.18^{o}$
c = 32.30
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 c.
Finding B:
We can use the Law of Sines.
$\frac{34}{sin(76^{o})} = \frac{21}{sin(B^{o})}$
Therefore, B = $36.82^{o}$
Finding C:
Since we found 2 other angles, we can use the fact that a triangle has angles that add to $180^{o}$.
180 - 76 - 36.82 = 67.18
Therefore, C = $67.18^{o}$
Finding c:
We can use the Law of Sines.
$\frac{34}{sin(76^{o})} = \frac{c}{sin(67.18^{o})}$
Therefore, c = 32.30
In total:
B = $36.82^{o}$
C = $67.18^{o}$
c = 32.30
