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Law of cosines and law of sines

Let $a$, $b$, and $c$ be the sides of a triangle.

Law of cosines. If $\theta $ is the angle between $a$ and $b$, then

MATHIf MATH, then $\cos \theta =0$ and we get the Pythagorean theorem.


Law of sines. If $A$, $B$, and $C$ are the angles opposite the sides $a$, $b$, and $c$, then

MATHIf $C=90\unit{\U{b0}}$, then $\sin C=1$ and we get $\sin A=a/c$; that is, the sine of an angle is equal to the opposite side over the hypotenuse.



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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.

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