Building a Skateboard Ramp

Date: 9/19/95 at 10:24:6
From: Anonymous
Subject: Skateboard ramp 

I'm trying to build a skateboard ramp, a pyramid with a flat top, 
a height of one foot, angle of ascent thirty degrees, other angles 
ninety degrees and sixty degrees.  If the height is one foot, what 
are the measurements of the other two sides of the triangle (the 
base and the slope) ?

- Thanks

Date: 9/25/95 at 16:35:36
From: Doctor Andrew
Subject: Re: Skateboard ramp 

FIGURE: A RIGHT TRIANGLE

     /|
    / | 
  z/  |
  /   |x
 /    |
/ a   |
--------
   y   

(a is an angle: 30, 60, etc)

Here are a couple of facts about this triangle that should help:

*  z^2 = x^2 + y^2.  (The Pythagorean Theorem)
   (so z = sqrt(x^2 + y^2))	

*  y = x / tan(a) 
    (tangent is a trigonometry function.  You can just use it on your
calculators.  To make life easier, tan 30 = 1/(sqrt(3)), tan 60 = 
sqrt(3),tan(45)=1)

So, if a is a 30 degree angle:

y = 1 ft /  tan(30) = 1 / (1/sqrt(3)) = sqrt(3) which is about 1.732 ft.

and if a is a 60 degree angle

y = 1 ft/ (tan(30)) = 1 / sqrt(3) = 1 /(1.732) = .577350 ft

Good luck!

-Doctor Andrew,  The Geometry Forum