An end to Sine Law and Cosine Law? OK not really... but there is a better way!
Consider a triangle with quadrances 16, 49, and 25. Determine the sum of the three spreads.
Quadrances are the square of the distances between vertices of the triangle. Spread gives one measure to the separation of two lines as a single dimensionless number in the range [0,1] (from parallel to perpendicular) for Euclidean geometry. It replaces the concept of angle but has several differences from angle, discussed in the section below. Spread can have several interpretations. Here is a helpful definition: .
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1 solution
The triangle has sides 4, 7, and 5. Law of cosines gives the cosines of the angles opposite these sides as 3 5 2 9 , − 5 1 , and 7 5 respectively.
sin 2 α + sin 2 β + sin 2 γ = 3 − cos 2 α − cos 2 β − cos 2 γ = 2 4 5 4 3 2