Question

how long should an escalator be if it is to make an angle of 41° with the floor and carry people a vertical distance of 24 feet between floors? round to at least 1 decimal place. feet question help: video ebook message instructor

Explanation:

Step1: Identify the trigonometric relationship

We know that the vertical distance is the opposite side ($y = 24$) and the escalator length ($L$) is the hypotenuse of a right - triangle. The sine function is given by $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here $\theta = 41^{\circ}$. So, $\sin(41^{\circ})=\frac{24}{L}$.

Step2: Solve for $L$

Rearrange the formula $\sin(41^{\circ})=\frac{24}{L}$ to get $L=\frac{24}{\sin(41^{\circ})}$.
We know that $\sin(41^{\circ})\approx0.6561$. Then $L=\frac{24}{0.6561}\approx36.6$.

Answer:

$36.6$