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单词 ProjectionFormula
释义

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

c=acosβ+bcosα,

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 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

acosα+bcosβ=ccosαcosβ.

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更新时间:2025/5/4 4:59:29