All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes
Two ways up (Posted on 2002-05-05) Difficulty: 3 of 5
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?

  Submitted by levik    
Rating: 2.7500 (4 votes)
Solution: (Hide)
The tower's radius actually plays no part in the problem.

The elevator will obviously move exactly 200 feet from the bottom of the tower to the top.

To calculate the length of the stairs, imagine it "uncoiled" from the tower, and flattened out on a flat surface. You will be looking at a right triangle with the height of 200 feet, and the angles of 30 and 60, where the length of the hypotenuse is what we are trying to find.

We can use a simple trigonometric equasion:
sin(A)/a = sin(B)/b, or
sin(90)/H = sin(30)/200 and
1/H = (1/2)/200, giving us
H = 400.

So the length of the stairway is only twice the length of the elevator shaft.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
No Subjectsam2019-03-01 03:51:25
answerK Sengupta2007-05-15 04:17:24
Hints/Tipsdoes spirality matters?Detti2004-10-06 12:04:19
xclent Qprashant2004-03-30 06:14:27
SolutionSolutionAntonio2003-08-24 04:05:48
Some ThoughtsNot Completely PossibleDrew Skau2003-08-20 14:19:05
hahahahatheBal2002-05-07 12:48:26
AgainAngela2002-05-07 07:25:17
AnswerAngela2002-05-07 07:23:01
Correctionnate2002-05-07 05:27:07
Sorry Richard :)nate2002-05-07 04:07:14
Two WaysRichard Gorman2002-05-06 14:08:18
Re: Answerlevik2002-05-06 10:49:13
AnswerAngela2002-05-06 09:03:10
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (5)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information