Question

Using the law of Cosines, in triangle DEF, if e=18 yd, d=10 yd, f=22 yd, find angle D

Answer 1

$d^2=e^2+f^2-2ef \cos D$

$d^2-e^2-f^2=-2ef \cos D$

$\cos D = \dfrac{e^2+f^2-d^2}{2ef}$

$\cos D = \dfrac{18^2+22^2-10^2}{2(18)(22)} = 59/66$

$D= \arccos \dfrac{59}{66} \approx 26.63^\circ$