Law of Sines
from class:
Algebra and Trigonometry
Definition
The Law of Sines is a trigonometric equation that relates the lengths of the sides of a triangle to the sines of its angles. It states that for any triangle, $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$, where $a$, $b$, and $c$ are the lengths of the sides opposite angles $A$, $B$, and $C$ respectively.
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5 Must Know Facts For Your Next Test
- The Law of Sines can be used to solve for unknown sides and angles in any triangle, not just right triangles.
- It is particularly useful in cases of oblique triangles (triangles without a right angle).
- The Law of Sines can lead to ambiguous cases (SSA condition) where two different triangles may satisfy the given conditions.
- To apply the Law of Sines, at least one angle-side opposite pair must be known.
- The formula can be rearranged to solve for an unknown angle: $\sin A = \frac{a \cdot \sin B}{b}$.
Review Questions
- How can you use the Law of Sines to find an unknown side in a triangle?
- What are ambiguous cases in the context of the Law of Sines?
- When applying the Law of Sines, what minimal information must you have about a triangle?
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