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 Two ways up (Posted on 2002-05-05)
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.

 Subject Author Date No Subject sam 2019-03-01 03:51:25 answer K Sengupta 2007-05-15 04:17:24 does spirality matters? Detti 2004-10-06 12:04:19 xclent Q prashant 2004-03-30 06:14:27 Solution Antonio 2003-08-24 04:05:48 Not Completely Possible Drew Skau 2003-08-20 14:19:05 hahahaha theBal 2002-05-07 12:48:26 Again Angela 2002-05-07 07:25:17 Answer Angela 2002-05-07 07:23:01 Correction nate 2002-05-07 05:27:07 Sorry Richard :) nate 2002-05-07 04:07:14 Two Ways Richard Gorman 2002-05-06 14:08:18 Re: Answer levik 2002-05-06 10:49:13 Answer Angela 2002-05-06 09:03:10

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