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The Law of Sines - Concept

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

One method for solving for a missing length or angle of a triangle is by using the law of sines. The law of sines, unlike the law of cosines, uses proportions to solve for missing lengths. The ratio of the sine of an angle to the side opposite it is equal for all three angles of a triangle. The law of sines works for any triangle, not just right triangles.

The law of sines applies to any kind of triangle not just right triangles and what it says is that there's a special relationship between the sine of an angle and the side opposite to it. So to be specific if I said the sine of a to side a, well that ratio will be equal to the sine of either b to side b or the sine of angle c to side c. So write this out its complete form, the law of sine says that the ration of sine of angle a to side a is equal to the ratio of sine of angle b to side b which is equal to the ratio of sine of angle c to side c. So this is pretty useful when you're trying to find missing sides or angles.

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