Vector Components

Any vector can be split into two perpendicular components, one along x and one along y. Together they make the original vector, tip to tail.

Fx drags the sled forward, Fy lifts it; together they rebuild F.

With $\theta$ measured from the x axis, the components are the sides of a right triangle:

$$F_x = F \cos\theta, \quad F_y = F \sin\theta$$

A rope pulls a sled with $40\ \mathrm{N}$ at $30^\circ$ above the ground. The part that drags the sled forward is $F_x = 40 \cos 30^\circ \approx 34.6\ \mathrm{N}$, and the part that lifts it is $F_y = 40 \sin 30^\circ = 20\ \mathrm{N}$.

Components make vectors easy to add: add all the x parts, then all the y parts.