Answer
A = $38.62^{o}$
B = $48.51^{o}$
C = $92.87^{o}$
Work Step by Step
Note: The Standard Form of the Law of Cosines is: $a^{2} = b^{2} + c^{2} - 2bc(cosA)$
Note: The Alternative Form of the Law of Cosines is: $cosA = \frac{b^{2} + c^{2} - a^{2}}{2bc}$
To solve the triangle, we need to find A, B, and C. We can use the Alternative Form of the Law of Cosines for each of the angles.
Finding A:
$cosA = \frac{12^{2} + 16^{2} - 10^{2}}{2(12)(16)}$
A = $38.62^{o}$
Finding B:
$cosB = \frac{10^{2} + 16^{2} - 12^{2}}{2(10)(16)}$
B = $48.51^{o}$
Finding C:
$cosC = \frac{10^{2} + 12^{2} - 16^{2}}{2(10)(12)}$
C = $92.87^{o}$
In Total:
A = $38.62^{o}$
B = $48.51^{o}$
C = $92.87^{o}$
