Question

Solve for c of the right triangle

Answer 1

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

Answer 2

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 = √(80-cos67)`