have a wall 2540mm high and wish to place a ladder at 75 degrees how far out would the base be from the wall?

Question

How is this calculated

Answer 1

The relationship between vertical height and horizontal length (for right triangle) is called the TANGENT of the angle.

We have 2540 mm vertical distance.
Assume 75 degrees is angle between ladder and horizontal surface.

Tangent (75 degrees) = 2540 / (horiz distance)

Therefore,
(Horiz distance) = 2540 / (tan(75))
= 680.59 mm

Note that this is the distance from the wall to the CENTER of the ladder footprint!

Answer 2

Using tangent and a right triangle

tangent (x) = vertical length / horizontal length