Answer
A = $31.87^{o}$
C = $136.13^{o}$
c = 210
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 A, c, and C.
Finding A:
We can use the Law of Sines.
$\frac{160}{sin(A^{o})} = \frac{63}{sin(12^{o})}$
Therefore, A = $31.87^{o}$
Finding C:
Since we are have 2 other angles, we can use the fact that a triangle has angles that add to $180^{o}$.
180 - 31.87 - 12 = 136.13
Therefore, C = $136.13^{o}$
Finding c:
We can use the Law of Sines.
$\frac{63}{sin(12^{o})} = \frac{c}{sin(136.13^{o})}$
Therefore, c = 210
In total:
A = $31.87^{o}$
C = $136.13^{o}$
c = 210
