$\"\"$

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One side of the right angle triangle is $\"\"$ cm.

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

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Consider the opposite angle as $\"\"$ .

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Here $\"\"$ .

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Possible error of the angle is $\"\"$ .

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Right angle triangle with given parameters :

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$\"\"$

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Consider

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$\"\"$

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Apply derivative on each side.

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$\"\"$ .

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Substitute $\"\"$ and $\"\"$ in the above expression.

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$\"\"$

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Error in the length of hypotenuse is $\"\"$ .

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$\"\"$

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(b)

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

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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

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$\"\"$

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(a) Error in the length of hypotenuse is $\"\"$ .

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(b) Percentage error in the length of the hypotenuse is $\"\"$ .