Para una acera de 2.50m de ancho, la altura de la rampa construida no debe exceder los 20m ¿Cuál es la pendiente de la rampa construida con estas medidas? ¿Y cuál el ángulo?

20.16  meters

82.77º

Step-by-step explanation:

We have that the ramp would have the shape of a rectangular triangle, where the height and width would be the legs and the slope the hypotenuse.

We can solve it by means of the Pythagorean theorem that tells us:

c ^ 2 = a ^ 2 + b ^ 2

a = 2.5 and b = 20, replacing:

c ^ 2 = 2.5 ^ 2 + 20 ^ 2

c ^ 2 = 406.25

c = 20.16

Therefore the slope would be 20.16 meters.

The angle, we will do it using the function: Sin A ° = opposite / hypotenuse

where the opposite is the height, that is to say 20 and the hypotenuse that is the slope is equal to 20.16, replacing:

Without Aº = 20 / 20.16

Without Aº = 0.992

 Aº = arc sin (0.992)

 Aº = 82.77

Which means that the angle is of the slope with the horizontal is 82.77º