Answer
$b = 5.26$
A = $102.44^{o}$
C = $37.56^{o}$
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 b:
$b^{2} = 8^{2} + 5^{2} - 2(8)(5)cos(40^{o})$
$b = 5.26$
We can use the Alternative Form of the Law of Cosines to find A:
$cosA = \frac{5.26^{2} + 5^{2} - 8^{2}}{2(5.26)(5)}$
A = $102.44^{o}$
We can use the Alternative Form of the Law of Cosines to find C:
$cosC = \frac{8^{2} + 5.26^{2} - 5^{2}}{2(8)(5.26)}$
C = $37.56^{o}$
In Total:
$b = 5.26$
A = $102.44^{o}$
C = $37.56^{o}$
