Stitz-Zeager_College_Algebra_e-book

On the curve r 2 2 sin however we reach the origin

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Unformatted text preview: c) sin(65◦ ) which yields sin(30◦ ) b = sin(65◦ ) 5.25 hence b = 5.25 sin(30◦ ) sin(65◦ ) ≈ 2.90 units. 764 Applications of Trigonometry β = 30◦ a ≈ 5.77 c = 5.25 a=7 β = 45◦ c ≈ 2.09 α = 120◦ γ = 15◦ α = 85◦ b ≈ 5.72 γ = 65◦ b ≈ 2.90 Triangle for number 1 Triangle for number 2 3. Since we are given (α, a) and c, we use the Law of Sines to find the measure of γ . We start ◦ with sin(γ ) = sin(30 ) and get sin(γ ) = 4 sin (30◦ ) = 2. Since the range of the sine function is 4 1 [−1, 1], there is no real number with sin(γ ) = 2. Geometrically, we see that side a is just too short to make a triangle. The next three examples keep the same values for the measure of α and the length of c while varying the length of a. We will discuss this case in more detail after we see what happens in those cases. 4. In this case, we have◦ the measure of α = 30◦ , a = 2 and c = 4. Using the Law of Sines, we get sin(γ ) = sin(30 ) so sin(γ ) = 2 sin (30◦ ) = 1. Now γ is an angle in a triangle w...
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