How to find if a triangle is acute or obtuse with side lengths?

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