Scaling a Right Triangle
Date: 12/01/2003 at 21:05:12 From: RedMan Subject: Right Triangle A right triangle has sides of length a = 30 ft, b = 8 ft, and c = 31.0483 ft. Next, side c is move inward 4 ft, while angles A, B, and C remain the same. How do I determine the new lengths of a, b, and c?
Date: 12/02/2003 at 20:29:44 From: Doctor Douglas Subject: Re: Right Triangle Hi RedMan. Thanks for writing to the Math Forum. Here is a diagram of the triangle: P--------------q-------Q PQ = a = 30 ft | . y PR = b = 8 ft r . RQ = c = 31.0483 ft R I assume you mean that line c is moved towards P by 4 ft, leading to new triangle Pqr. Consider point y, which lies on line RQ and is moved 4 ft inward to new point q on line PQ. qyQ is a right triangle, so yq = 4 ft = (qQ)*sin(Q) Thus, the top side PQ is shortened to become Pq, i.e., it becomes Pq = PQ - qQ = PQ - [4 ft / sin(Q)] Thus, each side of the original triangle is shrunk by multiplication by the following factor Pq (4 ft) 4 -- = 1 - ----------- = 1 - -------------- = 0.4825 PQ (PQ)*sin(Q) 30*(8/31.0483) Thus, Pq = 0.4825*(30 ft) = 14.47 ft Pr = 0.4825*(8 ft) = 3.86 ft rq = 0.4825*(31.0483 ft) = 14.98 ft Note that these sides still form a right triangle Pqr, and that it has the same angles (3.86/14.47) = (8/30). I hope that wasn't too complicated. - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/
Date: 12/11/2003 at 22:04:32 From: RedMan Subject: Thank you (Right Triangle) Thank you! Previously, this was performed by hand: first draw to scale, then calculate and count certain multiple objects. You've made my job much easier. It's good to have a flashlight for a dark path, but much better when someone shows you the light switch. Thanks ever so much. I'm sure to have another question, in the future. RedMan
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