Question

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?

Answer 1

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

Explanation:

`color(blue)("Condition 1")`

Let A be positive
Let B be negative as opposite direction

Magnitude of resultant is `24.9 - 20 = 4.9`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Condition 2")`

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(white)(xxxxxxxx)`

`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