One side of a right triangle is known to be 12 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.)(b) What is the percentage error? (Round your answer to the nearest integer.)

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Asked Nov 11, 2019
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One side of a right triangle is known to be 12 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.)


(b) What is the percentage error? (Round your answer to the nearest integer.)
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Expert Answer

Step 1

Part (a):

To estimate the error in the length of hypotenuse.

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One side of length is =12 cm. Opposite angle 30 degrees Error in angle ±1°

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Step 2

From the information,

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sin 0=°Pposite side hypotenuse hypotenuse °ppositeside sin 12 (i.e) h=- sin 1 =csc0 sin h=12csc0

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Step 3

Differentiate h with resp...

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h=12csc0 dh 12(-cot0csc)d0 dh-12cotOcscOd0 Let 0=30° de-is possible error in angle, Convert to radians d0 1°xT 180 = +0.0175

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