Overlapping right triangle problemDate: 09/14/97 at 22:57:51 From: Judy Wilson Subject: Overlapping right triangle problem Given right triangles ABC and DCB with rt angles at B and C. The hypotenuse of triangle ABC, AC, is 20 and the hypotenuse of triangle DCB, DB, is 30. The hypotenuses intersect at point E, which is a distance of 10 from BC. Find the length of BC. I've tried similar triangles and systems of trig equations, and I've gotten nowhere. Date: 09/15/97 at 14:19:56 From: Doctor Mitteldorf Subject: Re: Overlapping right triangle problem Dear Judy, I drew the figure three times before I recognized this as the old "two ladders in an alley" problem. One ladder is 20 feet, the other is 30 feet, they cross the alley in opposite directions, and they meet 10 feet off the ground. Here's a start: Call the width of the alley x+y, where x is the part to the left of the ladder and y is to the right. See if we can use both similar triangles and Pythagoras to generate two equations in x and y. The first equation, for example, says that the ratio of height to the base of the left "small" triangle is the same as the ratio of the height to the base of the "full" triangle formed by the alley, the right wall, and the ladder. 10/x = sqrt(30^2-(x+y)^2)/(x+y) I leave it to you to write down the corresponding equation for the other ladder, and to solve the two equations simultaneously for x and y. -Doctor Mitteldorf, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 09/15/97 at 15:57:58 From: Judy Ann Wilson Subject: Re: Overlapping right triangle problem Dear Dr. Mittledorf, Thanks so much for the help. I can hardly wait to go work on this. I knew the problem was a classic but... Judy |
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