Answer
B = $21.55^{o}$
C = $122.45^{o}$
c = 11.49
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, c, and B.
Finding B:
We can use the Law of Sines.
$\frac{8}{sin(36^{o})} = \frac{5}{sin(B^{o})}$
Therefore, B = $21.55^{o}$
Finding C:
Since we know 2 other angles, we can use the fact that a triangle has angles that add to $180^{o}$.
180 - 36 - 21.55 = 122.45
Therefore, C = $122.45^{o}$
Finding c:
We can use the Law of Sines.
$\frac{8}{sin(36^{o})} = \frac{c}{sin(122.45^{o})}$
Therefore, c = 11.49
In total:
B = $21.55^{o}$
C = $122.45^{o}$
c = 11.49
