So you want to find the length of the angle between 83 and 111. The best way to tackle this is to use sin, cos, and tan. I would start by finding the length of the angle between 83 and 165 first. The best method to use for this is cosine. Cosine is equal to Adjacent over Hypotenuse, so
cos x = 83 / 165.
cos x = 0.503
cos^-1 (0.503) = x
59.799 = x rounded 59.8 degrees.
Then the angle between 111 and 165. (I'll use sine for this one)
Sine = Opposite / Hypotenuse
sin y = 83 / 165
sin y = 0.503 ... notice it's the same number.
sin^-1 (0.503) = y
30.2 = y
Now that you know x is 59.8 degrees and y is 30.2 degrees, you can find the last angle.
59.8 + 30.2 = 90 degrees
180 - 90 = 90 degrees
So your final answer is, believe it or not, 90 degrees!
Hope that helps!
