A tower, 200 feet high, has an elevator inside it, and a spiral stairway winding its way around the tower at a constant 30 degree angle with the horisontal.

Given the tower's radius of 10 feet, what is the difference between the distance covered by a person going up in the elevator, versus one climbing the stairs?

I imagine a rectang of bottom 20*Pi=62.8318530718ft and a height of 200ft, we draw a 30 degree line at the lower left corner and measure the hypotenuse that results in the interior of the rectang. The rectang contains 5 rectangular triangles with an hypotenuse of 72.5519745694ft and one final rectangular triangle with an hypotenuse of 37.240127152ft. We just sum all hypotenuses and it gives 5*72.5519745694 + 37.240127152 = 400ft

The difference would be 400ft - 200ft = 200ft

Posted by Antonio on 2003-08-24 04:05:48