Answer
B = $9.43^{o}$
C = $25.57^{o}$
c = 10.53
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.
$\frac{14}{sin(145^{o})} = \frac{4}{sin(B^{o})}$
Therefore, B = $9.43^{o}$
Finding C:
Since we know 2 other angles, we can use the fact that a triangle has angles that add to $180^{o}$.
180 - 145 - 9.43 = 25.57
Therefore, C = $25.57^{o}$
Finding c:
We can use the Law of Sines.
$\frac{c}{sin(25.57^{o})} = \frac{14}{sin(145^{o})}$
Therefore, c = 10.53
In total:
B = $9.43^{o}$
C = $25.57^{o}$
c = 10.53
