Let a triangle have sides of length 
, 
,
and 
and let the angles opposite these sides be denoted 
, 
, and 
. The law of tangents states
![(a-b)/(a+b)=(tan[1/2(A-B)])/(tan[1/2(A+B)]).](/images/equations/LawofTangents/NumberedEquation1.svg) |
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)]).](/images/equations/LawofTangents/NumberedEquation2.svg) |
Law of Tangents
See also
Law of Cosines, Law of Sines, TangentExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Law of TangentsCite this as:
Weisstein, Eric W. "Law of Tangents." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LawofTangents.html