We have that,
The horizontal distance for the ramp = 12 feet.
Maximum height of the ramp = 1 feet.
So, we get that the value of the angle 'x' made by the ramp with the ground is given by,
i.e. x = 4.8°
Thus, the maximum angle made by the ramp with the ground is 4.8°.
I used (-) as theta; you solve this using your calculator
The maximum angle that a ramp can form with the ground is 4.76°.
Assuming the ramp as a right-angled triangle, and letting the horizontal distance being the leg adjacent and the vertical distance the leg opposite, then the tangent to the ramp angle will be:
The angle a is solving by the inverse of the leg's rate: