Question

you are building a ramp that must cover a horizontal distance of exactly 15 feet. the angle of the ramp from the ground is 19°. determine the length of the ramp, in feet. round to two decimal places as needed. show your work here

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the horizontal distance (adjacent side) is 15 feet, the angle with the ground is \(19^\circ\), and the length of the ramp is the hypotenuse (\(c\)). We use the cosine function, which is defined as \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos(19^\circ)=\frac{15}{c}\).

Step2: Solve for the hypotenuse (ramp length)

Rearranging the formula to solve for \(c\), we get \(c = \frac{15}{\cos(19^\circ)}\). First, calculate \(\cos(19^\circ)\) (make sure the calculator is in degree mode). \(\cos(19^\circ)\approx0.9455\). Then, \(c=\frac{15}{0.9455}\approx15.86\).

Answer:

\(15.86\)