Answer
$x^{o} \approx 47.3^{o}$
Work Step by Step
Apply law of cosines $b^2=a^2+c^2-2ac \cos B$
Need to solve for $B =x^{o}$
$2ac \cos x^{o}=a^2+c^2-b^2$
This implies $x^{o}=\cos^{-1}(\dfrac{a^2+c^2-b^2}{2ac})$
Plug the given values to obtain:
$x^{o}=\cos^{-1}(\dfrac{a^2+c^2-b^2}{2ac})$
$x^{o}=\cos^{-1}(\dfrac{(19)^2+(12)^2-(14)^2}{2 \times 19 \times 12})$
$x^{o}=\cos^{-1}(\dfrac{309}{456})$
In order to calculate the value, we will use calculator in degree mode.
$x^{o} \approx 47.3^{o}$
