Law of Sines
المؤلف:
Abramowitz, M. and Stegun, I. A.
المصدر:
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover
الجزء والصفحة:
...
12-10-2019
2281
Law of Sines
Let 
, 
, and 
be the lengths of the legs of a triangle opposite angles 
, 
, and 
. Then the law of sines states that
 |
(1)
|
where 
is the radius of the circumcircle. Other related results include the identities
 |
(2)
|
 |
(3)
|
the law of cosines
 |
(4)
|
and the law of tangents
![(a+b)/(a-b)=(tan[1/2(A+B)])/(tan[1/2(A-B)]).](http://mathworld.wolfram.com/images/equations/LawofSines/NumberedEquation5.gif) |
(5)
|
The law of sines for oblique spherical triangles states that
 |
(6)
|
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, p. 148, 1987.
Coxeter, H. S. M. and Greitzer, S. L. "The Extended Law of Sines." §1.1 in Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 1-3, 1967.
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