# 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?

Nov 14, 2015

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

#### Explanation:

$\textcolor{b l u e}{\text{Condition 1}}$

Let A be positive
Let B be negative as opposite direction

Magnitude of resultant is $24.9 - 20 = 4.9$

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

$\textcolor{b l u e}{\text{Condition 2}}$

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

$\textcolor{b r o w n}{\text{Resolve all the horizontal vector components}}$

${R}_{\text{horizontal}} = \left(24.9 \times \frac{\sqrt{3}}{2}\right) - \left(20 \times \sin \left(20\right)\right)$

$\textcolor{w h i t e}{\times \times \times \times}$

$\textcolor{b r o w n}{\text{Resolve all the vertical component of the resultant}}$

${R}_{\text{vertical}} = \left(24.9 \times \sin \left(30\right)\right) - \left(20 \times \cos \left(20\right)\right)$

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