Answer
A = $26.38^{o}$
B = $36.34^{o}$
C = $117.28^{o}$
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:
$cosA = \frac{8^{2} + 12^{2} - 6^{2}}{2(8)(12)}$
A = $26.38^{o}$
Finding B:
$cosB = \frac{6^{2} + 12^{2} - 8^{2}}{2(6)(12)}$
B = $36.34^{o}$
Finding C:
$cosC = \frac{8^{2} + 6^{2} - 12^{2}}{2(8)(6)}$
C = $117.28^{o}$
In Total:
A = $26.38^{o}$
B = $36.34^{o}$
C = $117.28^{o}$
