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Is the statement true or false? The Law of Sines and Law of Cosines can be used to...

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novjb | Salutatorian

Posted July 30, 2013 at 10:06 PM via web

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Is the statement true or false?

The Law of Sines and Law of Cosines can be used to find angle and side measures in any angle.

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted July 31, 2013 at 1:29 AM (Answer #1)

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Depending on the given information, you can use the Law of Sines or the Law of Cosines to find missing side lengths or angle measures in any triangle.

Your question says angle. If the question asks about any angle, then it is false. Both of the laws deal with triangles and thus the angles are forced to be between `0^@` and `180^@` .

If the question asks about any triangle, it is true if there is sufficient information given. You need at least 3 of the six pieces of information, with at least 1 side length. (There are 3 side lengths and 3 angle measures -- you need at least 1 side and any other 2 pieces of information.)

You would use the Law of Sines if you know ASA,AAS, or SSA.

You would use Law of Cosines if you know SSS, SAS, or SSA.

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I would say that the answer is false. If you are given the three angle measures of a triangle, neither method will give you the side lengths. (Becuase there are an infinite number of triangles with the same angle measures and different side lengths.)

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