Answer
A = $132.77^{o}$
B = $31.91^{o}$
C = $15.32^{o}$
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:
$cosA = \frac{1.8^{2} + 0.9^{2} - 2.5^{2}}{2(1.8)(0.9)}$
A = $132.77^{o}$
Finding B:
$cosB = \frac{2.5^{2} + 0.9^{2} - 1.8^{2}}{2(2.5)(0.9)}$
B = $31.91^{o}$
Finding C:
$cosC = \frac{2.5^{2} + 1.8^{2} - 0.9^{2}}{2(2.5)(1.8)}$
C = $15.32^{o}$
In Total:
A = $132.77^{o}$
B = $31.91^{o}$
C = $15.32^{o}$
