I'm guessing by vertical distance you mean how high the ramp goes, and you're looking for how far the ramp stretches horizontally.
First let's draw a picture to help us visualize it (see picture). The height of the ramp is 30in. The angle that the ramp makes with the ground is 20°. The height of the ramp and the ground makes a 90° angle. You're trying to find the length of the green arrow.
To do this, you will need your trigonometric ratios. Remember SOHCAHTOA:
[tex]sin\theta = \frac{opposite}{hypotenuse} \\
cos\theta = \frac{adjacent}{hypotenuse} \\
tan\theta = \frac{opposite}{adjacent} [/tex]
where θ = angle board makes with the ground. Your opposite side is across from the angle θ, your adjacent side is beside the angle θ, and is shorter than the hypotenuse, which is the longest side.
Judging from our picture, θ = 20°, the side opposite it is the height of the triangle = 30in, and we are looking for the adjacent side. That means will be using tangent. Plug out numbers into the equation for tangent to find the length of the adjacent side:
[tex]tan\theta = \frac{opposite}{adjacent}\\
tan20 = \frac{30}{adjacent}\\
adjacent = \frac{30}{tan20}\\
adjacent = 82.4 \: in[/tex]
The length of the horizontal is 82.4 in.
