Answer
A = $91.80^{o}$
B = $44.10^{o}$
C = $44.10^{o}$
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:
$cosA = \frac{52.5^{2} + 52.5^{2} - 75.4^{2}}{2(52.5)(52.5)}$
A = $91.80^{o}$
Finding B:
$cosB = \frac{75.4^{2} + 52.5^{2} - 52.5^{2}}{2(75.4)(52.5)}$
B = $44.10^{o}$
Finding C:
$cosC = \frac{75.4^{2} + 52.5^{2} - 52.5^{2}}{2(75.4)(52.5)}$
C = $44.10^{o}$
In Total:
A = $91.80^{o}$
B = $44.10^{o}$
C = $44.10^{o}$
