# calculus

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three forces with magnitudes 100, 50, and 80 lb act on an object at angles of 50 degree, 160 degree, and -20 degree respectively. ind the direction and magnitude o the resultant force.

• calculus -

express each as a vector in component form

magnitude 100,direction 50
= (100cos50, 100sin50) = (64.279 , 76.604)
mag50,direction160
= (-8.682 , 17.101
mag80, direction -20
= ( 75.175 , -27.361)

= (130.772 , 66.344)

magnitude = √(x^2 + y^2) = 146.638
direction :
tan Ø = 66.344/130.772
Ø = 26.9° or 333.1°
but my sketch showed the resultant to be in the first quadrant, so
Ø = 26.9°

• calculus -

mag50,direction160 = (-46.985,17.101)

• calculus -

you messed up mag50, direction160
=(-46.984, 17.101

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