A force of 100 N is acting at 30 degrees to the horizontal. Find the horizontal and vertical components of the force.

We'll decompose the vector of force to x and y axis. The
angle made by the force with x axis is of 30 degrees.

The
horizontal component of the force is the adjacent side, next to the angle of 30
degrees.

The vertical component of the force is the
opposite side to the angle of 30 degrees.

The given vector
of the force represents the hypotenuse of the right angle triangle, whose legs are the
components of the vector of force.

We'll determine the
component, using the sine and cosine functions.

Let Fx be
the horizontal component and Fy be the vertical
component.

sin 30 = Fy/F => Fy = F*sin 30 = 100/2 =
50 N

cos 30 = Fx/F => Fx = F*cos 30 = 100*sqrt3/2 =
50*sqrt3N

The requested horizontal and
vertical components of the given vector of force are: Fx = 50*sqrt3N and Fy =
50N.