A straight wheelchair ramp rises 3 feet over a horizontal distance of 12 feet. If is the angle the ramp makes with the horizontal ground, which of the following is true?

SAT Right triangles and trigonometry Practice Question 8 (Medium)

Question bank / Right triangles and trigonometry

Math · Geometry and TrigonometryMedium

A straight wheelchair ramp rises $3$ feet over a horizontal distance of $12$ feet. If $\theta$ is the angle the ramp makes with the horizontal ground, which of the following is true?

$\sin\theta = \frac{1}{4}$

$\cos\theta = \frac{1}{4}$

$\tan\theta = 4$

$\tan\theta = \frac{1}{4}$

Show answer and explanation

Answer: D

The rise ( $3$ feet) is opposite $\theta$ , and the horizontal distance ( $12$ feet) is adjacent to $\theta$ . So $\tan\theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{3}{12} = \frac{1}{4}$ .

Choice A treats $12$ feet as the length of the ramp (the hypotenuse), but $12$ feet is the horizontal distance.

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