Answer:
75.5°
Step-by-step explanation:
You want the angle between a 50 pound force and a 75 pound force given that their resultant is a 100 pound force. Force 1 is aligned with the +x axis, and Force 2 is in the first quadrant.
Law of Cosines
The forces and their resultant form a triangle such that the angle opposite the resultant is the supplement of the angle between the forces. We can find the angle opposite the resultant using the law of cosines:
c² = a² +b² -2ab·cos(C)
cos(C) = (a² +b² -c²)/(2ab)
C = arccos(a² +b² -c²)/(2ab) = arccos((50² +75² -100²)/(2·50·75))
C = arccos(-1875/7500) = arccos(-1/4) ≈ 104.48°
The angle between the vectors is the supplement of this:
angle12 = 180° -104.48° = 75.52° ≈ 75.5°
The angle between the forces is about 75.5°.
