Oh, looks like these forces are competing in a "pulling contest". Let's see if we can find the angle where they'll be the most tangled up!
First, let's draw a sketch. We have two forces, Force 1 = 60 pounds and Force 2 = 90 pounds, forming a triangle with the resultant force.
Now, we can use the law of cosines to find the angle between the forces. In this case, the magnitude of the resultant force is 50 pounds, so we can set up the equation:
50^2 = 60^2 + 90^2 - 2(60)(90) * cos(theta)
Simplifying that equation, we get:
2500 = 3600 + 8100 - 10800 * cos(theta)
Now, let's rearrange and isolate the cosine(theta):
-6100 = -10800 * cos(theta)
cos(theta) = -6100 / -10800
cos(theta) = 0.56481481
To find the angle, we need to take the inverse cosine (cos^-1) of 0.56481481.
Using a calculator, the angle comes out to be approximately 55.55 degrees.
Rounding to the nearest degree, the angle between the forces would be about 56 degrees.