An airplane flies from point A to point B. Point A is 40 kilometers from a ground signal at point C. Point
B is 56 kilometers from the same ground signal. If AB = 80 kilometers, find the measure of ACB to
the nearest degree.

  112°

Step-by-step explanation:

The law of cosines can be used to find angle C from the three side lengths. The usual formulation of that law is ...

  c^2 = a^2 + b^2 -2ab·cos(C)

Then the angle C can be found to be ...

  C = arccos((a^2 +b^2 -c^2)/(2ab))

For the given side lengths,

  C = arccos((40^2 +56^2 -80^2)/(2·40·56)) = arccos(-1664/4480)

  C ≈ 112°