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

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SUMMARY

The discussion centers on the side ratios of a 30:60:90 triangle, specifically the ratio of 1 : √3 : 2. A participant mistakenly refers to a triangle with angles of 30 and 40 degrees, which is mathematically impossible. The correct understanding is that multiplying the side ratios by integers maintains the Pythagorean identity, except when multiplied by 4, due to an arithmetic error. Participants emphasize the importance of careful mathematical reasoning and the implications of misconceptions in geometry.

PREREQUISITES
  • Understanding of basic triangle properties
  • Familiarity with Pythagorean theorem
  • Knowledge of trigonometric ratios in right triangles
  • Basic arithmetic skills for manipulating ratios
NEXT STEPS
  • Study the properties of 30:60:90 triangles
  • Learn about the Pythagorean theorem and its applications
  • Explore common arithmetic errors in geometry
  • Investigate the implications of angle measures in triangle classification
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Students of geometry, mathematics educators, and anyone interested in understanding triangle properties and avoiding common mathematical misconceptions.

DeusAbscondus
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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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