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Mathematics LibreTexts

8: Further Applications of Trigonometry

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    In this chapter, we will explore applications of trigonometry that will enable us to solve many different kinds of problems, including finding the height of a tree. We extend topics we introduced in Trigonometric Functions and investigate applications more deeply and meaningfully.

    • 8.1: Non-right Triangles - Law of Sines
      In this section, we will find out how to solve problems involving non-right triangles. The Law of Sines can be used to solve oblique triangles. According to the Law of Sines, the ratio of the measurement of one of the angles to the length of its opposite side equals the other two ratios of angle measure to opposite side. There are three possible cases: ASA, AAS, SSA. Depending on the information given, we can choose the appropriate equation to find the requested solution.
    • 8.2: Non-right Triangles - Law of Cosines
      Unfortunately, while the Law of Sines enables us to address many non-right triangle cases, it does not help us with triangles where the known angle is between two known sides, a SAS (side-angle-side) triangle, or when all three sides are known, but no angles are known, a SSS (side-side-side) triangle. In this section, we will investigate another tool for solving oblique triangles described by these last two cases.
    • 8.3: Vectors in 2D
      Introduction to 2D Vectors - geometric and algebraic approaches to sketching, component form, magnitude, direction, scalar multiplication, addition and subtraction, unit vectors, standard unit vectors
    • 8.4: Vectors in Three Dimensions
      A revisit of an introduction to vectors, but in 3 dimensions rather than two.
    • 8.5: The Dot Product
      Evaluation of the dot product, finding the angle between vectors, projection of one vector onto another, and work applications
    • 8.6: The Cross Product
      In this section, we develop an operation called the cross product, which allows us to find a vector orthogonal to two given vectors. Use the cross product to find the area of a parallelogram.


    8: Further Applications of Trigonometry is shared under a CC BY license and was authored, remixed, and/or curated by LibreTexts.

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