$\"\"$

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Measurement of one side of the right angle triangle is $\"\"$ .

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Angle opposite to that side is $\"\"$ .

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$\"\"$

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Thus, $\"\"$ and $\"\"$ .

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Consider the length of the hypotenuse as $\"\"$ .

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$\"\"$

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$\"\"$ .

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Consider $\"\"$ .

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$\"\"$

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Differentiate the above equation with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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(a) Approximate the percentage error in computing the length of the hypotenuse:

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$\"\"$

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$\"\"$

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Percentage error in computing the length of the hypotenuse $\"\"$ .

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$\"\"$

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(b)

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Estimate the maximum allowable percent error in measuring the angle if the error in computing the length of the hypotenuse cannot exceed $\"\"$ .

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$\"\"$

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Find $\"\"$ .

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$\"\"$

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The maximum allowable percent error in measuring the side is $\"\"$ .

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$\"\"$

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(a) Percentage error in computing the length of the hypotenuse $\"\"$ .

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(b) The maximum allowable percent error in measuring the side is $\"\"$ .