Question

What is the Law of Sines and what is the Law of Cosines?

Accepted Answer

The **Law of Sines** relates the ratio of a triangle’s side length and corresponding angle measurement to each other side length and corresponding angle measurement.    
It is defined algebraically as:   

$$\frac{a}{\sin\;A} = \frac{b}{\sin\;B} = \frac{c}{\sin\;C}$$    

where *a*, *b*, and *c* are side lengths, and *A*, *B*, and *C* are the angles opposite them, respectively.

The **Law of Cosines** relates the side lengths of a triangle to the cosine measurement of one of its angles.    
It is equivalently stated in 3 forms, depending on the side lengths and angle measurement known:

$$a^2 = b^2 + c^2 - 2bc\cos\;A$$,   

$$b^2 = a^2 + c^2 - 2ac\cos\;B$$, and   

$$c^2 = a^2 + b^2 - 2ab\cos\;C$$, where *a*, *b*, and *c* are side lengths, and *A*, *B*, and *C* are their opposite angles, respectively.

Flashcard 14 - Next Generation Advanced Algebra and Functions Flashcard Set for the ACCUPLACER Test

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