Answer
A = $30.11^{o}$
B = $43.16^{o}$
C = $106.73^{o}$
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:
$cosA = \frac{15^{2} + 21^{2} - 11^{2}}{2(15)(21)}$
A = $30.11^{o}$
Finding B:
$cosB = \frac{11^{2} + 21^{2} - 15^{2}}{2(11)(21)}$
B = $43.16^{o}$
Finding C:
$cosC = \frac{11^{2} + 15^{2} - 21^{2}}{2(11)(15)}$
C = $106.73^{o}$
In Total:
A = $30.11^{o}$
B = $43.16^{o}$
C = $106.73^{o}$
