In order to solve this triangle we must use cosine law: [tex]c^{2} = a^{2} + b^{2} - 2ab*cosC[/tex]
Now let's plug in the values we are given: [tex]c^{2} = 5^{2} + 8^{2} - 2(5)(8) * cos 67[/tex] [tex]c^{2} = 25 + 64 - 80*cos67[/tex] [tex]c = \sqrt{80-cos67}[/tex]
From the Law of Cosines, we know b=8 a=5 angle C=67 side c² = a² + b² -2ab • cos(C) side c² = 5^2 +8^2 -2*5*8 * cos (67) side c² = 25 + 64 -(80*.39073) side c² = 89 -
31.2584
side c² = 57.7416
side c =
7.5987893773
