projection formula
Theorem. Let , , be the sides of a triangle and , the angles opposing , , respectively. Then one has
independently whether the angles are acute, right or obtuse.
Knowing the way to determine the length of the projection (http://planetmath.org/ProjectionOfPoint) of a line segment, the truth of the theorem is apparent; the below illustrate the cases where is acute and obtuse (cosine of an obtuse angle
is negative).
Note. Especially, if neither of and is right angle, the formula of the theorem may be written