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Half-side formula : ウィキペディア英語版
Half-side formula

In spherical trigonometry, the half side formula relates the angles and lengths of the sides of spherical triangles, which are triangles drawn on the surface of a sphere and so have curved sides and do not obey the formulas for plane triangles.〔.〕
==Formulas==
The half-side formulas are〔.〕
:
\begin
\tan\left(\frac\right) & = R \cos (S- \alpha) \\()
\tan \left(\frac\right) & = R \cos (S- \beta) \\()
\tan \left(\frac\right) & = R \cos (S - \gamma)
\end

where
* ''a'', ''b'', ''c'' are the lengths of the sides respectively opposite ''α'', ''β'', ''γ'',
* S = \frac(\alpha +\beta + \gamma) is half the sum of the angles, and
* R=\sqrt}.
The three formulas are really the same formula, with the names of the variables permuted.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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