Lesson 2: The Sine and Cosine Ratios - Setting up Ratios

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A video demonstration of the solution for Example 1 is provided.


EXAMPLE 1

State and evaluate the tangent ratio, the sine ratio, and the cosine ratio for the acute angle provided in the diagram.



Solution


Step 1: Identify and label the sides as being adjacent to, opposite and hypotenuse in relation to the angle indicated.



Step 2: State the appropriate ratios.

Tangent Sine Cosine
\(\begin{align} \text{tan}\,\theta&=\frac{\text{Opposite}}{\text{Adjacent}} \\ \\ \text{tan}\,30°&=\frac{82}{142} \\ \\ \text{tan}\,30°&=0.577 \\ \end{align}\) \(\begin{align} \text{sin}\,\theta&=\frac{\text{Opposite}}{\text{Hypotenuse}} \\ \\ \text{sin}\,30°&=\frac{82}{164} \\ \\ \text{sin}\,30°&=0.5 \\ \end{align}\) \(\begin{align} \text{cos}\,\theta&=\frac{\text{Adjacent}}{\text{Hypotenuse}} \\ \\ \text{cos}\,30°&=\frac{142}{162} \\ \\ \text{cos}\,30°&=0.866 \\ \end{align}\)


Now, it is your turn! Complete the questions in your Chapter 3, Lesson 2 Practice Makes Perfect that refer to Setting Up Ratios.



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