MHB Discovering the Truth Behind the Side Ratios of a 30:40:90 Triangle

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The discussion centers on the side ratios of a right triangle, specifically questioning the validity of multiplying the ratio 1:√3:2 by various integers while maintaining the Pythagorean identity. It is clarified that a triangle with angles of 30 and 40 degrees cannot exist, as the correct angles for the given side ratios are 30, 60, and 90 degrees. An arithmetic error was acknowledged by one participant, leading to confusion over the triangle's classification. The conversation also touches on the intersection of mathematics and belief systems, highlighting a participant's surprise at the coexistence of faith and mathematical understanding in some individuals. Overall, the thread emphasizes the importance of accuracy in mathematical discussions.
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(Plse bear with me: until i learn how to fly this thing, / must stand for radical)

If the side ratio for a 30:40:90 deg right triangle are 1 : /3 : 2
then, is the following true:

one may multiply this ratio by 1,2,3 or 5,6,7,8,9 or 10 and the pythagorean identity obtains but NOT by 4

If so, why not?

Thx,
Godfree
 
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DeusAbscondus said:
(Plse bear with me: until i learn how to fly this thing, / must stand for radical)

If the side ratio for a 30:40:90 deg right triangle are 1 : /3 : 2
then, is the following true:

one may multiply this ratio by 1,2,3 or 5,6,7,8,9 or 10 and the pythagorean identity obtains but NOT by 4

If so, why not?

Thx,
Godfree

A right triangle cannot have 30 and 40 degrees for its other two angles, in fact if the side rations of a triangle are \(1,\ \sqrt{3},\ 2\) then it is a 30,60,90 degree triangle

CB
 
Thank's Cap'n; it was an arithmetic error, that was all...
I'll be more careful before posting next time... sheeesh, i wasted 4 hours looking at this today, and kept making the same tiny error in my math...
Anyway, i heartily concur with Epicurius' sentiments and, by inference, your core values: i find a lot in common with non-believers, with atheists actually (why be coy) but I'm constantly amazed at how people (like my teacher) can do higher maths and still believe in invisible friends in the sky, and hold a young Earth model in the same brain. Enough off-topic.
Thanks again,
 
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