projection formula

Theorem.  Let a, b, c be the sides of a triangle and α, β the angles opposing a, b, respectively.  Then one has


independently whether the angles are acute, right or obtuse.

Knowing the way to determine the length of the projection ( of a line segmentMathworldPlanetmath, the truth of the theorem is apparent; the below illustrate the cases where β is acute and obtuse (cosine of an obtuse angleMathworldPlanetmathPlanetmath is negative).

Note.  Especially, if neither of α and β is right angle, the formula of the theorem may be written

Title projection formula
Canonical name ProjectionFormula
Date of creation 2013-03-22 18:27:11
Last modified on 2013-03-22 18:27:11
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 9
Author pahio (2872)
Entry type Theorem
Classification msc 51N99
Synonym projection formula for triangles
Related topic BaseAndHeightOfTriangle