Question

An architect is designing a department store. She wants to add an escalator. She knows that the escalator will make a 30° angle with the floor and will have a vertical height of 36 feet. How much room will she need to allot for the horizontal length? The horizontal length needed is Answer feet. What distance will a person travel on the excalator stairs? The distance a person would travel on the escalator stairs is Answer feet.

Answer 1

As per the problem

The escalator make a 30° angle with the floor .

The escalator have a vertical height of 36 feet.

Now draw the diagram with the given information, the diagram is attached below

From the diagram,

Horizontal length=AB=d

Distance traveled by the person on the escalator stairs=AC=l

In triangle ABC,

$tan30=\frac{36}{d}\\ \\ \frac{1}{\sqrt{3}} = \frac{36}{d}\\ \\ d=36\sqrt{3}$

Again in triangle ABC, Using Pythagoras Theorem

$AC^2=AB^2+BC^2\\ \\ l^2=36^2+(36\sqrt{3})^2\\ \\ l=\sqrt{36^2+(36\sqrt{3})^2} \\ \\ l=\sqrt{5184} =72$

The horizontal length needed is $36\sqrt{3} ft$

The distance a person would travel on the escalator stairs is 72 ft