Question

Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100°, respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

Answer 1

The direction and magnitude can be found by summing the x- and y-components of each force.
It is best presented in the form of a table, where
x-component = Fcos(theta)
y-component = Fsin(theta)
For F=25 pounds, angle = 30
25cos(30)=21.65

Force  angle     x-component          y-component
25       30         25cos(30)=21.65    25sin(30)=12.5
30       100       30cos(100)=-5.21   30sin(100)=29.54
Total                Fx=16.44                 Fy=42.04
Therefore angle = tan^(-1)(Fy/Fx)=tan^(-1)(42.04/16.44) = 68.64 °
magnitude = sqrt(Fx^2+Fy^2)=sqrt(16.44^2+42.04^2)=45.15 pounds