Loterre: Mathématiques: law of sines

geometry > spherical geometry > spherical trigonometry > law of sines

geometry > Euclidean geometry > trigonometry > law of sines

law of sines

In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law,
${\\displaystyle {\ rac {a}{\\sin {\\alpha }}}\\,=\\,{\ rac {b}{\\sin {\eta }}}\\,=\\,{\ rac {c}{\\sin {\\gamma }}}\\,=\\,2R,}$
where $a, b$ , and $c$ are the lengths of the sides of a triangle, and $α, β$ , and $γ$ are the opposite angles (see figure 2), while $R$ is the radius of the triangle's circumcircle. When the last part of the equation is not used, the law is sometimes stated using the reciprocals;
${\\displaystyle {\ rac {\\sin {\\alpha }}{a}}\\,=\\,{\ rac {\\sin {\eta }}{b}}\\,=\\,{\ rac {\\sin {\\gamma }}{c}}.}$
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Law_of_sines)

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