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Lesson 69 of 1524

Further Applications of Trigonometry

The Law of Sines can be used to solve oblique triangles, which are non-right triangles

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The Law of Sines can be used to solve oblique triangles, which are non-right triangles The ambiguous case arises when an oblique triangle can have different outcomes

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 The Law of Sines can be used to solve triangles with given criteria

Law of Sines — states that the ratio of the measurement of one angle of a triangle to the length of its opposite side is equal to the remaining two ratios of angle measure to opposite side; any…. ambiguous case — a scenario in which more than one triangle is a valid solution for a given oblique SSA triangle. oblique triangle — any triangle that is not a right triangle. cardioid — a member of the limaçon family of curves, named for its resemblance to a heart; its equation is given as r = a ± b cos θ and r = a ± b sin θ , where a b = 1.

Be able to find an expression for x such that the domain of the set of parametric equations remains the same as the original rectangular equation.

Worked example

What does “Law of Sines” mean in Further Applications of Trigonometry?

  1. 1Use the wording this chapter gives for Law of Sines.
  2. 2The book says: states that the ratio of the measurement of one angle of a triangle to the length of its opposite side is equal to the remaining two ratios of angle measure to opposite side; any….
  3. 3Do not use the meaning of ambiguous case. That term means a scenario in which more than one triangle is a valid solution for a given oblique SSA triangle.

Result: states that the ratio of the measurement of one angle of a triangle to the length of its opposite side is equal to the remaining two ratios of angle measure to opposite side; any…

Why. That is the meaning this chapter gives for Law of Sines.

Do not swap Law of Sines and ambiguous case. Law of Sines means states that the ratio of the measurement of one angle of a triangle to the length of its opposite side is equal to the remaining two ratios of angle measure to opposite side; any…. ambiguous case means a scenario in which more than one triangle is a valid solution for a given oblique SSA triangle.

Practice margin

This chapter

A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.