Answer
a = 12.20
B = $10.54^{o}$
C = $121.46^{o}$
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:
$a^{2} = 3^{2} + 14^{2} - 2(3)(14)cos(48^{o})$
a = 12.20
Finding B:
$cosB = \frac{12.20^{2} + 14^{2} - 3^{2}}{2(12.20)(14)}$
B = $10.54^{o}$
Finding C:
$cosC = \frac{12.20^{2} + 3^{2} - 14^{2}}{2(12.20)(3)}$
C = $121.46^{o}$
In Total:
a = 12.20
B = $10.54^{o}$
C = $121.46^{o}$
