Question

Para la construcción de un nuevo centro comercial de dos niveles,de 6m de altura cada uno,se están acondicionando dos escaleras mecánicas (subida y bajada) el ingeniero encargado de la obra sugiere que debe tener una pendiente m=1/√3,como máximo. ¿cual sera la longitud de la escalera eléctrica?

Answer 1

The length of the electrical stairs is 2 meters.

Explanation:

This problem is about the length of a electrical stairs.

We know that its slope is
`m=(1)/(√(3) )`, but we know the slope can be defined as

`tan \theta = m`

Where
`\theta` is the elevation angle. Replacing the slope we have

`tan\theta = (1)/(√(3) )`

Additionally, we know that the tangent trigonometric reason is defined as

`tan \theta = (opposite)/(adjacent)`

This means the opposite leg to the elevation angle is 1, and the adjacent leg is the square root of 3. Knowing and using Pythagorean's Theorem, we can find the hypothenuse (which models the length of the electrical stairs)

`h^(2)=1^(2) +(√(3) )^(2) \\h=√(1+3)= √(4)=2`

Therefore, the length of the electrical stairs is 2 meters.