A road rises 24 meters for every 100 meters of horizontal distance. If is the angle the road makes with the horizontal, which choice gives the value of in simplest form?

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SAT Right Triangles & Trigonometry Question 37 | Free SAT Prep | Aniko

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Question 37·Easy·Right Triangles and Trigonometry

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A road rises 24 meters for every 100 meters of horizontal distance. If $\theta$ is the angle the road makes with the horizontal, which choice gives the value of $\tan\theta$ in simplest form?

When a problem describes an incline as “rises A for every B horizontal,” treat it as a right triangle with opposite $=A$ and adjacent $=B$ , so $\tan\theta=\frac{A}{B}$ . Then reduce the fraction completely if the question asks for simplest form.

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Connect tangent to slope

For an incline, $\tan\theta$ is the ratio $\dfrac{\text{vertical change}}{\text{horizontal change}}$ .

Use the given rise and run

The road rises 24 meters (rise) over 100 meters (run), so start with $\frac{24}{100}$ .

Reduce to simplest form

Simplify $\frac{24}{100}$ by dividing top and bottom by a common factor greater than 1.

Desmos Guide

Compute the rise/run ratio

Type 24/100 into Desmos to compute the value of the ratio.

Check which option is simplest

Enter each answer choice (for example, 6/25, 24/100, 25/6, 12/50) and note which one matches 24/100 and is already fully reduced.

Step-by-step Explanation

Write $\tan\theta$ as rise over run

The tangent of an incline angle is the ratio of vertical change to horizontal change:

\tan\theta=\frac{\text{rise}}{\text{run}}=\frac{24}{100}.

Simplify the fraction

Divide numerator and denominator by their greatest common factor, $4$ :

\frac{24}{100}=\frac{6}{25}.

Therefore, $\tan\theta=\frac{6}{25}$ .

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Step-by-step Explanation

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Step-by-step Explanation