Answer
$m \angle F \approx 47.2^{o}$
Work Step by Step
Apply law of cosines $f^2=d^2+e^2-2de \cos F$
Need to solve for $F$
$2de \cos F=d^2+e^2-f^2$
This implies $F=\cos^{-1}(\dfrac{d^2+e^2-f^2}{2de})$
Plug the given values to obtain:
$F=\cos^{-1}(\dfrac{(12)^2+(10)^2-(9)^2}{2 \times 12 \times 10}) \\=\cos^{-1}(\dfrac{163}{240})$
In order to calculate the value, we will use calculator in degree mode.
$m \angle F \approx 47.2^{o}$
