Solving the right triangle

Solving the right triangle

  1. Can the Law of Sines be used to solve a right triangle? Write a short paragraph explaining why it can or cannot be used. If it can be used, explain how to use it. Is there an easier way to solve the triangle? Explain.
  2. Describe how the Law of Cosines can be used to solve the ambiguous case of the oblique triangle ABC, where a = 12 feet, b = 30 feet, and A = 20°. Is the result the same as when the Law of Sines is used to solve the triangle? Describe the advantages and the disadvantages of each method.
  3. a) In your own words, state the difference between a scalar and a vector. Give examples of each. b) Give geometric descriptions of the operations of addition of vectors and multiplication of a vector by a scalar.

4. What is known about Θ, the angle between two nonzero vectors u and v, if each of the following is true? Explain your answers.

a) u • v = 0

b) u • v > 0

c) u • v < 0

5. The famous formula shown below is called Euler’s formula, after the Swiss mathematician Leonhard Euler (1707-1783).

e^a + bi = e^a(cos b + i sin b)

This formula gives rise to the equation e^πi + 1 = 0. This equation related the five most famous numbers in mathematics–0, 1,π , e, and i– in a single equation. Show how Euler’s formula can be used to derive this equation. Write a short paragraph summarizing your work.

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