Question

an escalator in a mall carries people a vertical distance of 22 feet between floors. how long is the escalator if it makes an angle of 30° with the ground? round to the nearest foot, if necessary.

Explanation:

Step1: Identify the trigonometric relation

We know the vertical distance (opposite side to the given angle) and we want to find the length of the escalator (hypotenuse). We use the sine - function. $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 30^{\circ}$ and the opposite side $y = 22$ feet, and let the hypotenuse be $l$. So, $\sin30^{\circ}=\frac{22}{l}$.

Step2: Solve for the hypotenuse

Since $\sin30^{\circ}=\frac{1}{2}$, we have the equation $\frac{1}{2}=\frac{22}{l}$. Cross - multiply to get $l\times1=22\times2$.

Answer:

44