Answer
A = $42.06^{o}$
B = $12.90^{o}$
C = $125.04^{o}$
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:
$cosA = \frac{3^{2} + 11^{2} - 9^{2}}{2(3)(11)}$
A = $42.06^{o}$
Finding B:
$cosB = \frac{9^{2} + 11^{2} - 3^{2}}{2(9)(11)}$
B = $12.90^{o}$
Finding C:
$cosC = \frac{9^{2} + 3^{2} - 11^{2}}{2(9)(3)}$
C = $125.04^{o}$
In Total:
A = $42.06^{o}$
B = $12.90^{o}$
C = $125.04^{o}$
