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

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The correct answer is:

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.


Explanation:

Both the Law of Sines and the Law of Cosines are used to solve triangles containing unknown side lengths and angle measurements. In conjunction with the fact that the internal angles of a triangle sum to \(180^\circ\), many triangles can be solved.

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