Answer
c = 13.87
A = $43.28^{o}$
B = $28.72^{o}$
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 Standard and Alternative Form of the Law of Cosines to solve the triangle.
Finding c:
$c^{2} = 10^{2} + 7^{2} - 2(10)(7)cos(108^{o})$
c = 13.87
Finding A:
$cosA = \frac{7^{2} + 13.87^{2} - 10^{2}}{2(7)(13.87)}$
A = $43.28^{o}$
Finding B:
$cosB = \frac{10^{2} + 13.87^{2} - 7^{2}}{2(10)(13.87)}$
B = $28.72^{o}$
In Total:
c = 13.87
A = $43.28^{o}$
B = $28.72^{o}$
