Question

Solve for c of the right triangle

Answer 1

In order to solve this triangle we must use cosine law:
$c^{2} = a^{2} + b^{2} - 2ab*cosC$

Now let's plug in the values we are given:
$c^{2} = 5^{2} + 8^{2} - 2(5)(8) * cos 67$
$c^{2} = 25 + 64 - 80*cos67$
$c = \sqrt{80-cos67}$

Answer 2

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