Force Vectors

Calculate the resultant magnitude from the three coplanar forces below.

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

$$$R_{x}=3N+5cos(110)N+0N=3N-1.71N=1.29N$$$
$$$R_{y}=3N+5 sinā”(110)N+0N=3N+4.69N=7.69N$$$
Finally, to solve for the magnitude:
$$$R=\sqrt{{R_{x}}^{2}+{R_{y}}^{2}}=\sqrt{(1.29N)^{2}+(7.69N)^{2}}=\sqrt{60.8N^{2}}=7.8N$$$
7.8N