Which choice is equal to for the triangle shown?

Solution available with step-by-step explanation

SAT Right Triangles & Trigonometry Question 13 | Free SAT Prep | Aniko

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Question 13·Easy·Right Triangles and Trigonometry

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Which choice is equal to $\tan\theta$ for the triangle shown?

Use SOHCAHTOA. Since the question asks for $\tan\theta$ , label the side opposite $\theta$ and the side adjacent to $\theta$ (not the hypotenuse), then take the ratio opposite/adjacent.

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Locate the angle

Angle $\theta$ is at point $A$ . Only use the sides that touch or face that angle.

Pick the correct sides

The opposite side is directly across from $\theta$ . The adjacent side touches $\theta$ but is not the hypotenuse.

Use the definition of tangent

Use $\tan\theta=\dfrac{\text{opposite}}{\text{adjacent}}$ .

Desmos Guide

Enter the tangent ratio as a fraction

In Desmos, type 3/4 and press enter to see its value.

Match to an answer choice

Compare the fraction you entered to the four choices and select the one that matches exactly.

Step-by-step Explanation

Identify opposite and adjacent to $\theta$

Angle $\theta$ is at vertex $A$ . The side opposite $\theta$ is $\overline{BC}$ (length $3$ ), and the side adjacent to $\theta$ is $\overline{AC}$ (length $4$ ).

Use the tangent ratio

By definition,

\tan\theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{3}{4}.

So the correct choice is $\frac{3}{4}$ .

Strategy

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Step-by-step Explanation

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Step-by-step Explanation