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Gerald B.
guest

May2008, 12:15 PM (EST) 

"Constucting a triangle instructions"

Dear Alex, I’ve been enjoying your mathfocused website. I ran across this explanation for triangle construction given an angle “A”, an opposite side “a” and a height (at “A”) of “h”. I’m trying to follow the instructions but keep getting stuck at the first part. I just can’t figure out how to “Construct an arc (part of a circle) subtending segment BC = a such that for every point A on it, angle BAC equals the given angle A” How do I choose the radius of the arc or its starting point? Any hints? Insructions from the site: Construct an arc (part of a circle) subtending segment BC = a such that for every point A on it, angle BAC equals the given angle A. Draw a line parallel to BC at the distance ha. There could be 0,1, or 2 points of intersection of the line with the arc. In the latter case solutions are mirror images of each other; so even then there is at most one solution. 

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Gerlad B.
guest

May2008, 01:31 PM (EST) 

2. "RE: Constucting a triangle instructions"
In response to message #1

OK I think I get it. Say angle A = 30 degrees. (Forget a and h for the moment). On a clock face, I find that if I put A’ at the centre, legs coming out at 30 degree angles cross the other edge of the clock one hour apart (say 6 and 7 o’clock). What I take from this is the radius of the clock and the linear distance between 6 and 7 (not in hours!). That gives me a ratio. Now, I am given the linear distance BC=a, so I can scale up my clock so that B’C’: BC = R’:R 

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