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| | Im Marisa and was born on 14 March 1972. My hobbies are American football and Gongoozling.<br><br>Feel free to surf to my web-site [http://www.freshwidewallpapers.com/profile/elwid essay service] |
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| [[Image:Law-of-haversines.svg|right|thumb|Spherical triangle]]
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| In [[spherical trigonometry]], the '''half side formula''' relates the angles and lengths of the sides of [[spherical triangle]]s, which are triangles drawn on the surface of a sphere and so have curved sides and do not obey the formulas for plane triangles.
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| ==Formulas==
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| : <math>
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| \begin{align}
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| \tan\left(\frac{a}{2}\right) & = R \cos (S- \alpha) \\[8pt]
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| \tan \left(\frac{b}{2}\right) & = R \cos (S- \beta) \\[8pt]
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| \tan \left(\frac{c}{2}\right) & = R \cos (S - \gamma)
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| \end{align}
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| </math>
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| where
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| * ''a'', ''b'', ''c'' are the lengths of the sides respectively opposite ''α'', ''β'', ''γ'',
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| * <math>S = \frac{1}{2}(\alpha +\beta + \gamma)</math> is half the sum of the angles, and
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| * <math>R=\sqrt{\frac {-\cos S}{\cos (S-\alpha) \cos (S-\beta) \cos (S-\gamma)}}.</math>
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| The three formulas are really the same formula, with the names of the variables permuted.
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| == See also ==
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| * [[Spherical law of cosines]]
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| [[Category:Spherical trigonometry]]
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Latest revision as of 23:47, 8 November 2014
Im Marisa and was born on 14 March 1972. My hobbies are American football and Gongoozling.
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