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4: The Law of Sines and The Law of Cosines

  • Page ID
    37223
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    Previously, we used the fundamental trigonometric relationships in right triangles to find unknown distances and angles. Unfortunately, in many problem solving situations, it is inconvenient to use right triangle relationships. Therefore, from the right triangle relationships, we can derive relationships that can be used in any triangle.

    • 4.1: The Law of Sines
      The Law of sines is based on right triangle relationships that can be created with the height of a triangle.
    • 4.2: The Law of Sines - The Ambiguous Case
      Multiple answers arise when we use the inverse trigonometric functions. For problems in which we use the Law of sines given one angle and two sides, there may be one possible triangle, two possible triangles or no possible triangles. There are six different scenarios related to the ambiguous case of the Law of sines: three result in one triangle, one results in two triangles and two result in no triangle.
    • 4.3: The Law of Cosines
    • 4.4: Applications

    Thumbnail: Law of cosines with acute angles. (CC BY SA 3.0 Unported; Scaler via Wikipedia)


    This page titled 4: The Law of Sines and The Law of Cosines is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Richard W. Beveridge.

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