Answer
c = 11.06
A = $51.79^{o}$
B = $23.21^{o}$
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:
$c^{2} = 9^{2} + 4.5^{2} - 2(9)(4.5)cos(105^{o})$
c = 11.06
Finding A:
$cosA = \frac{4.5^{2} + 11.06^{2} - 9^{2}}{2(4.5)(11.06)}$
A = $51.79^{o}$
Finding B:
$cosB = \frac{9^{2} + 11.06^{2} - 4.5^{2}}{2(9)(11.06)}$
B = $23.21^{o}$
In Total:
c = 11.06
A = $51.79^{o}$
B = $23.21^{o}$
