Tangent Side Length Ratios Examples

Lesson 1: The Tangent Ratio - Tangent Side Length Ratios Examples

   Multimedia

A video describing the use of the tangent ratio table is provided.

EXAMPLE 1

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The ratios for angle measures of 35° and 50° have been left blank in the table from the previous section. Draw a right triangle with an acute angle of 35°, and measure the opposite and adjacent side lengths. Use these lengths to calculate the \(\frac{\text{length opposite}\,\theta}{\text{length adjacent to}\,\theta}\) ratio for 35°. Repeat this process for 50°. Complete the table on the previous page.

Solution

The ratio for 35° is approximately 0.70, and the ratio for 50° is approximately 1.19

EXAMPLE 2

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Use the table from the previous section to state a ratio of sides for each of the following triangles. Explain what each ratio represents.

1. 


2. 

Solution

1. The value produced when the length of the side opposite 25° is divided by the length of the side adjacent to 25° is 0.47


2. The value produced when the length of side b is divided by the length of side a is 2.14

EXAMPLE 3

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Use the table from the previous section to determine the values of the variables.

1. 


2. 

Solution

1. \(\frac{6}{6}=1,\,\text{so}\,x=45°\)


2. \(\frac{42.0}{15.3}=2.75,\,\text{so}\,y=70°\)

EXAMPLE 4

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Use the table from the previous section to determine the value of the unknown variable, to the nearest tenth, in the triangle shown.

Solution

\(\begin{align} \frac{\text{length opposite 20°}}{\text{length adjacent to 20°}}&=0.36 \\ \\ \frac{v}{15}&=0.36 \\ \\ \frac{v}{\cancel{15}}\times \cancel{\color{red}{15}}&=0.36\times {\color{red}{15}} \\ \\ v&=5.4 \\ \end{align}\)




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