Vector A has length 24.9 and is at an angle of 30 degrees. Vector B has length 20 and is at an angle of 210 degrees. To the nearest tenth of a unit, what is the magnitude of A+B?

1 Answer
Nov 14, 2015

Not totally defined where the angles are taken from so 2 possible conditions.
Resolved into vertical and horizontal components


#color(blue)("Condition 1")#
Tony B

Let A be positive
Let B be negative as opposite direction

Magnitude of resultant is #24.9 - 20 = 4.9#


#color(blue)("Condition 2")#

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Let to the right be positive
Let to the let be negative

Let up be positive
Let down be negative

Let the resultant be R

#color(brown)("Resolve all the horizontal vector components")#

#R_("horizontal") =(24.9 times (sqrt(3))/2 ) - (20 times sin(20))#


#color(brown)("Resolve all the vertical component of the resultant")#

#R_("vertical") = (24.9 times sin(30)) - (20 times cos(20))#

With these two values available you should be able to determine the magnitude and direction of the resultant