MHB Use differentials to estimate the error

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To estimate the error in computing the hypotenuse of a right triangle with one side measuring 20 cm and an opposite angle of 30° (with a possible error of ±1°), differentials can be applied. The calculation involves determining the derivative of the hypotenuse length with respect to the angle and multiplying it by the error in the angle measurement. The estimated error in the hypotenuse length is found to be approximately ±0.10 cm. The percentage error is then calculated based on the estimated hypotenuse length, yielding a result of about ±1%. This method effectively demonstrates how small changes in angle measurements can impact the calculated length of the hypotenuse.
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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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