# the resultant of two force f and 60n is 80n inclined at 60° to 60n determine magnitude and direction of F

Arun
25758 Points
3 years ago

Dear student,
The resultant force would be given by:
$R=\sqrt{80^{2}+60^{2}+2\left ( 80 \right )\left ( 60 \right )cos\left ( 60^{0} \right )}=\sqrt{6400+3600+2\times 80\times 60\times \frac{1}{2}}=\sqrt{14800}=121.655 N$
The direction would be given by:
Now, lets place the 60 N force along the horizontal direction so the 80 N force would be making an angle of 60 degree.
Hence if we say that the resultant force is making an angle $\alpha$ with the horizontal, we would get:
$Fcos\alpha =60+80cos60; Fsin\alpha=80 sin60$Taking a ratio, would give the required result.

Regards
Arun