Answer
$c= 12.72$
A = $47.61^{o}$
B = $62.39^{o}$
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 Form of the Law of Cosines to find c:
$c^{2} = 10^{2} + 12^{2} - 2(10)(12)cos(70^{o})$
$c= 12.72$
We can use the Alternative Form of the Law of Cosines to find A:
$cosA = \frac{12^{2} + 12.72^{2} - 10^{2}}{2(12)(12.72)}$
A = $47.61^{o}$
We can use the Alternative Form of the Law of Cosines to find B:
$cosB = \frac{10^{2} + 12.72^{2} - 12^{2}}{2(10)(12.72)}$
B = $62.39^{o}$
In Total:
$c= 12.72$
A = $47.61^{o}$
B = $62.39^{o}$
