# 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^circ with the ground?

Jun 27, 2017

The escalator is $40$ feet long

#### Explanation:

So this is our problem:

Remeber
$S \in = \frac{o p p}{h y p}$

$C o s = \frac{a \mathrm{dj}}{h y p}$

$T a n = \frac{o p p}{a \mathrm{dj}}$

$\textcolor{w h i t e}{0}$

$S \in \left({30}^{o}\right) = \frac{20}{h y p}$

$\frac{20}{\sin} \left({30}^{o}\right) = h y p$

$\frac{20}{\frac{1}{2}} = h y p$

$40 = h y p$

The escalator -- or hypotenuse-- is $40$ feet long