# Resultant Force?

a force F1 of 35 newtons pulls at an angle of 15 degrees notrth of due east. A force F2 of 75 newtons pulls at an angle of 55 degrees west of due south. Find the magntiude and direction of the resultant force.

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1. probably easier for you to do this on x, y axis system

First find x and y components of first force (15deg above x axis)
F1x = 35 cos 15
F1y = 35 sin 15

now the second force(90-55) = 35 below -x axis)
F2x = -75 cos 35
F2y = -75 sin 35
Fx = 35 cos 15 -75 cos 35 = -27.6
Fy = 35 sin 15 -75 sin 35 = -34.0

F^2 = Fx^2+Fy^2
so F = 43.7 in magnitude
tan theta = Fy/Fx = -43/-27.6
in quadrant 3 because both are negative
so theta = 57.3 deg below -x axis
or 57.3 deg south of west
or 90-57.3 = 32.7 deg west of south

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posted by Damon
2. Ah, thank you so much! You're a lifesaver! Thank you and God bless you for taking the time to help!

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