Lesson 1: The Tangent Ratio: Using the Tangent Ratio with the Calculator


Recall the steps used to solve for the side length or the angle measure when using trigonometric ratios.

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

Step 2: State the appropriate ratio.

Step 3: Substitute known values and calculate the unknown value.

EXAMPLE 1

Determine the value of p to the nearest hundredth.



Solution


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



Step 2: State the appropriate ratio.

\(\text{tangent of angle}\,\theta=\frac{\text{length opposite}\,\theta}{\text{length adjacent to}\,\theta}\)

Step 3: Substitute known values and calculate the unknown value.

\(\begin{align} \text{tan}\,\theta&=\frac{\text{opp}}{\text{adj}} \\ \\ \text{tan}\,26°&=\frac{p}{35} \\ \\ {\color{red}{35}}\times \text{tan}\,26°&=\frac{p}{\cancel{35}}\times \cancel{\color{red}{35}} \\ \\ 17.070...&=p \\ \end{align}\)

Notice that you will get a slightly different, and less accurate answer if you evaluate and round tan26° in the second step of the solution.

\(\begin{align} \text{tan}\,\theta&=\frac{\text{opp}}{\text{adj}} \\ \\ \text{tan}\,26°&=\frac{p}{35} \\ \\ {\color{red}{35}}\times 0.49&=\frac{p}{\cancel{35}}\times \cancel{\color{red}{35}} \\ \\ 17.15&=p \\ \end{align}\)

Most calculators will allow you to evaluate 35 • tan26° in one step by entering one of the following.
35 × tan26 enter or =
35 × 26 tan =

It is preferable to leave any rounding until the very last step in a solution.

The value of p is 17.07 (not 17.15).


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