Answer
A = $39.35^{o}$
B = $16.75^{o}$
C = $123.90^{o}$
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:
$cosA = \frac{25^{2} + 72^{2} - 55^{2}}{2(25)(72)}$
A = $39.35^{o}$
Finding B:
$cosB = \frac{35^{2} + 72^{2} - 25^{2}}{2(55)(72)}$
B = $16.75^{o}$
Finding C:
$cosC = \frac{55^{2} + 25^{2} - 72^{2}}{2(55)(25)}$
C = $123.91^{o}$
In Total:
A = $39.35^{o}$
B = $16.75^{o}$
C = $123.91^{o}$
