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Calculus

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the measurement on one side of a right triangle is found to be 9.5 inches inches, and the angle opposite that side is 27 degrees,45' with a possible error of 15'. (round answers to two decimal places)

a) Approximate the percent error in computing the length of the hypotenuse.

b) Estimate the maximum allowable percent error in measuring the angle of the error in computing the length of the hypotenuse cannot exceed 1%

  • Calculus -

    27°45' = 27.75° = 0.484 radians
    15' = .25° = 0.00436 radians

    the hypotenuse h is

    h = 9.5 cscθ
    h(.484) = 20.416

    dh = -9.5 cscθ cotθ dθ
    for dh <= 1% at θ=.484
    .00484 >= 9.5(2.149)(1.902) dθ
    dθ <= 0.012%

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