Question

1. (18) an escalator in a department store is to carry people a vertical distance of 20 feet between floors. how long is the escalator if it makes an angle of 30° with the ground? include units with your answer.

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the vertical distance (opposite side to the 30° angle) is 20 feet, and the length of the escalator is the hypotenuse (\(c\)). We use the sine function: \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 30^\circ\), opposite \(= 20\) ft, and hypotenuse \(= c\) (length of escalator). So \(\sin(30^\circ)=\frac{20}{c}\).

Step2: Solve for \(c\)

We know that \(\sin(30^\circ)=\frac{1}{2}\). Substituting into the equation: \(\frac{1}{2}=\frac{20}{c}\). Cross - multiplying gives \(c\times1 = 20\times2\).

Answer:

The length of the escalator is 40 feet.