Question

score on last try: 0 of 1 pts. see details for more. get a similar question you can retry this question below a skateboard ramp must be set up to rise from the ground 30°. if the height from the ground to the platform is 20 feet, how far away from the bottom of the platform must the ramp be set? round your answer to the nearest hundredth.

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the height (opposite side to the 30° angle) is 20 ft, and we need to find the adjacent side (let's call it \( x \)) to the 30° angle. The tangent function relates the opposite and adjacent sides: \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \).

Step2: Set up the equation

For \( \theta = 30^\circ \), opposite = 20 ft, adjacent = \( x \). So \( \tan(30^\circ) = \frac{20}{x} \). We know that \( \tan(30^\circ) = \frac{1}{\sqrt{3}} \approx 0.5774 \).

Step3: Solve for \( x \)

Rearranging the equation: \( x = \frac{20}{\tan(30^\circ)} \). Substituting the value of \( \tan(30^\circ) \), we get \( x = \frac{20}{\frac{1}{\sqrt{3}}} = 20\sqrt{3} \approx 20\times1.732 = 34.64 \) (rounded to the nearest hundredth).

Answer:

34.64