A force of 60lbs acts on an object at an angle of 40 degrees

A force of 60lbs acts on an object at an angle of 40 degrees. A second force of 85lbs acts on an object at an angle of -20 degrees. Find the magnitude of the resulting force.

Solution

force of 60lbs acts at an angle of 40 degrees

second force of 85lbs acts at an angle of -20 degrees

angle between two force = 50 + 70 = 120 degrees

therefore, applying law of cosines to find the resultant force

R^2 = 60^2 + 85^2 - 2(60)(85) cos 120

R^2 = 10825 + 5100

R = 126.194 magnitude