How to find the length of a quarter pipe with a transition radius of 70 in and a height of 40 in
The Pythagorean theorem shows that for all
right triangles with a hypotenuse (longest side) of length c,
and remaining sides of length a and b, the following equation is true:
So we make a right triangle:
As you can see above, the hypotenuse ( longest edge ) of the triangle is the transition radius of 70 in, the length of the second edge (vertical) is equal to the height minus the transition radius, 40-70=30 in, and the length of the third edge is unknown and what we are trying to solve for.
All that remains is to substitute a=length, b=30 in, and c=70 in into the Pythagorean theorem and solve for length.