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Law of Tangents


Let a triangle have sides of length a, b, and c and let the angles opposite these sides be denoted A, B, and C. The law of tangents states

 (a-b)/(a+b)=(tan[1/2(A-B)])/(tan[1/2(A+B)]).

An analogous result for oblique spherical triangles states that

 (tan[1/2(a-b)])/(tan[1/2(a+b)])=(tan[1/2(A-B)])/(tan[1/2(A+B)]).

See also

Law of Cosines, Law of Sines, Tangent

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References

Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 79, 1972.Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 145 and 149, 1987.

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Law of Tangents

Cite this as:

Weisstein, Eric W. "Law of Tangents." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LawofTangents.html

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