Estimate the hypotenuse of the triangle

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SUMMARY

The discussion centers on estimating the hypotenuse of a triangle with sides measuring 5 and 12 using differentials to determine the maximum error. The hypotenuse is calculated as 13, with the error expressed as 13 ± Error. Participants confirm that while the hypotenuse can be stated as 13, the focus is on accurately determining the maximum error through differential calculus. This approach allows for an estimation that incorporates potential inaccuracies.

PREREQUISITES
  • Basic understanding of the Pythagorean theorem
  • Familiarity with differential calculus concepts
  • Knowledge of error analysis in mathematical estimations
  • Ability to perform basic algebraic calculations
NEXT STEPS
  • Study the Pythagorean theorem and its applications in geometry
  • Learn about differentials and their role in estimating errors
  • Explore error analysis techniques in mathematical problems
  • Practice calculating hypotenuses and associated errors with various triangle dimensions
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Students in mathematics, educators teaching geometry and calculus, and anyone interested in understanding error estimation in mathematical calculations.

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Hi I just had a question on a quiz that asked to estimate the hypotenuse of triangle with given sides and a maximum error possibility. The two given sides were 5 and 12..i don't need an exact solution..but I was just wondering how to do it.

I Found the maximum Error that was possible and the said the the hypotenuse was 13+/-Error. Is this how to do it?

The max error was found using differentials.
 
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Assuming that you did in fact find "Error", then yes, the hypotenuse would be [itex]13\pm "Error"[/itex]. The point of the problem is, of course, to find "Error".
 
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Yeah that's what I thought..But I didnt know if you were allowed to simply say the hypotenuse was 13..since finding that has nothing to do with differentials...I wasnt sure if there was actually a way to find the actual estimated length of it...without having to subtract the errror.
 

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