# Vector

A rope is wrapped around a pole so that a force of 75 lbs acts on one end and a force of 53 lbs acts on the other end. If the angle between the two forces is 114 degrees what is the resultant force? What angle does the resultant force make with the 53 lbs force?

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#### Solution Preview

Let the direction of the 53 LBS force be the x axis

Angle between the two forces = 114 degrees

x component of the 75 LBS force= 75 Cos 114 = -30.51 LBS

y component of the 75 LBS force= 75 Sin 114 = 68.52 LBS

Total force in the x direction= 22.49 LBS =53-30.51

Total force in the y direction= 68.52 LBS

Resultant force = square root of {(x component)^2 + (y component)^2}= ...

#### Solution Summary

Finds the magnitude and the direction of the resultant force.

$2.19