Answer:
In the figure attached we can see in a better way this situation. If we are told the rope is at 60 degress to the horizontal, we can place this rope in the origin of the X-Y coordinate system.
If we observe in detail, we have a right triangle where the opposite side [tex]OS[/tex] to the angle [tex]60\º[/tex] is the vertical component [tex]F_{y}[/tex] and the adjacent side [tex]AS[/tex] is the horizontal component [tex]F_{x}[/tex] . So, we can use trigonometric functions to find the force [tex]F[/tex] (the hypotenuse [tex]h[/tex]) applied to the rope.
For [tex]F_{x}[/tex]:
We can use the trigonometric function cosine, which is defined as:
[tex]cos(60\º)=\frac{AS}{h}[/tex]
This means [tex]F_{x}=Fcos(60\º)[/tex]
[tex]F_{x}=300Ncos(60\º)[/tex]
[tex]F_{x}=150N[/tex]
For [tex]F_{y}[/tex]:
We can use the trigonometric function sine, which is defined as:
[tex]sin(60\º)=\frac{OS}{h}[/tex]
This means [tex]F_{y}=Fsin(60\º)[/tex]
[tex]F_{y}=300Nsin(60\º)[/tex]
[tex]F_{y}=259.8N[/tex]
Finally the horizontal and vertical components are 150 N and 259.8 N
