Answer
a = 18.59
B = $23.79^{o}$
C = $126.21^{o}$
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 a:
$a^{2} = 15^{2} + 30^{2} - 2(15)(30)cos(30^{o})$
a = 18.59
Finding B:
$cosB = \frac{18.59^{2} + 30^{2} - 15^{2}}{2(18.59)(30)}$
B = $23.79^{o}$
Finding C:
$cosC = \frac{18.59^{2} + 15^{2} - 30^{2}}{2(18.59)(15)}$
C = $126.21^{o}$
In Total:
a = 18.59
B = $23.79^{o}$
C = $126.21^{o}$
