Answer
a = 11.27
B = $27.45^{o}$
C = $32.55^{o}$
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 a:
$a^{2} = 6^{2} + 7^{2} - 2(6)(7)cos(120^{o})$
a = 11.27
Finding B:
$cosB = \frac{11.27^{2} + 7^{2} - 6^{2}}{2(11.27)(7)}$
B = $27.45^{o}$
Finding C:
$cosC = \frac{11.27^{2} + 6^{2} - 7^{2}}{2(11.27)(6)}$
C = $32.55^{o}$
In Total:
a = 11.27
B = $27.45^{o}$
C = $32.55^{o}$
