This construction is commonly called "dropping a perpendicular" and is well used in fortification drawing; in many cases, as when constructing Chevalier de Ville's method of fortifying a bastion front, the accuracy of one's dropped perpendiculars are critical to a correct and proportional representation of a concrete idea.

Given a right line (AB) and an external point (C) construct a second line that passes through Point C and is perpendicular to Line AB.

Using Point C as center describe an arc of a circle that cuts through Line AB at two points (D and E). It is important that Point D and Point E are equi-distant from Point C, otherwise the whole thing gets messed up.

Opening the compass to a length equal to the distance between Points C and D and using Points C and D as centers, describe two arcs that intersect at Point F on the opposite side of Line AB from Point C.

Produce a right line that connects Point C and Point F that intersects Line AB.

Mark the point of intersection as Point E and shorten Line CF to Point G to define Line CG. Line CG is perpendicular to Line AB.

~ An Instructive Animation Wherein the Foregoing Construction is Visually Explained ~