Vector Magnitudes

Calculate the resultant magnitude from the three coplanar forces below.

Hint
$$$R=\sqrt{{R_{x}}^{2}+{R_{y}}^{2}}$$$
Hint 2
To find the total forces both in the x and y directions:
$$$R_{x}=\sum F_{xi}$$$
$$$R_{y}=\sum F_{yi}$$$
$$$i=A,B,C$$$
To find the total forces both in the x and y directions.
$$$R_{x}=\sum F_{xi}$$$
$$$R_{y}=\sum F_{yi}$$$
$$$i=A,B,C$$$

$$$R_{x}=2N+3cos(100)N+0N=2N-0.52N=1.47N$$$
$$$R_{y}=2N+3 sinā”(100)N+0N=2N+2.95N=4.95N$$$
Finally, to solve for the magnitude:
$$$R=\sqrt{{R_{x}}^{2}+{R_{y}}^{2}}=\sqrt{(1.47N)^{2}+(4.95N)^{2}}=\sqrt{26.67N^{2}}=5.16\:N$$$
5.16 N