Answer
B = $56.24^{o}$
C = $3.76^{o}$
c = 1.89
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.
$\frac{25}{sin(120^{o})} = \frac{24}{sin(B^{o})}$
Therefore, B = $56.24^{o}$
Finding C:
Since we found 2 other angles, we can use the fact that a triangle has angles that add to $180^{o}$.
180 - 120 - 56.24 = 3.76
Therefore, C = $3.76^{o}$
Finding c:
We can use the Law of Sines.
$\frac{25}{sin(120^{o})} = \frac{c}{sin(3.76^{o})}$
Therefore, c = 1.89
In total:
B = $56.24^{o}$
C = $3.76^{o}$
c = 1.89
