Use differentials to estimate the error

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SUMMARY

This discussion focuses on using differentials to estimate the error in calculating the hypotenuse of a right triangle with one side measuring 20 cm and an opposite angle of 30°, subject to a ±1° error. The differential method yields an estimated error in the hypotenuse length, which is calculated and rounded to two decimal places. Additionally, the percentage error is determined and rounded to the nearest integer, providing a clear understanding of the impact of angle measurement inaccuracies on hypotenuse length.

PREREQUISITES
  • Understanding of basic trigonometry, specifically sine and cosine functions.
  • Familiarity with the concept of differentials in calculus.
  • Knowledge of error estimation techniques in mathematical calculations.
  • Ability to perform basic arithmetic operations and rounding.
NEXT STEPS
  • Study the application of differentials in various geometric contexts.
  • Explore advanced trigonometric functions and their derivatives.
  • Learn about error propagation in measurements and calculations.
  • Investigate real-world applications of differential calculus in engineering and physics.
USEFUL FOR

Students in mathematics or engineering, educators teaching trigonometry and calculus, and professionals involved in precision measurement and error analysis.

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One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30°, with a possible error of ±1°.
(a) Use differentials to estimate the error in computing the length of the hypotenuse. (Round your answer to two decimal places.)
±...cm(b) What is the percentage error? (Round your answer to the nearest integer.)
±... %
 
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