triangle solving
Let us consider skew-angled triangles. If one knows three parts of a triangle, among which at least one side, then the other parts may be calculated by using the law of sines and the law of cosines. We distinguish four cases:
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1.
ASA. Known two angles and one side, e.g. , , . Other parts:
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2.
SSS. Known all sides , , . The angles are obtained from
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3.
SAS. Known two sides and the angle between them, e.g. , , . Other parts from
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4.
SSA. Known two sides and the angle of one of them, e.g. , , . Other parts are gotten from
Since the SSA criterion alone does not prove congruence, it is not surprising that there may not always be a single solution for here. In fact, if the first equation gives , then the situation is impossible and the triangle does not exist. If the equation gives , one gets two distinct values of ; an acute and an obtuse . If in this case , then there are two different triangles as , but if , then there is only one triangle.
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http://svn.gold-saucer.org/repos/PlanetMath/TriangleSolving/triangle.mpMetaPost source code for the above diagrams
Title | triangle solving |
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Canonical name | TriangleSolving |
Date of creation | 2013-03-22 15:44:02 |
Last modified on | 2013-03-22 15:44:02 |
Owner | stevecheng (10074) |
Last modified by | stevecheng (10074) |
Numerical id | 11 |
Author | stevecheng (10074) |
Entry type | Definition |
Classification | msc 51-00 |
Related topic | Congruence |