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# One side of a right triangle is known to be $20 cm$ long and the opposite angle is measured as $30^o,$ with a possible error of $\pm 1^o.$(a) Use differentials to estimate the error in computing the length of the hypotenuse.(b) What is the percentage error?

## (a) estimated error: $\pm 1.209 \mathrm{cm}$(b) percentage error: $\pm 3 \%$

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

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### Video Transcript

Okay, Part A. We know that D h. The differential is negative. 20 coast seeking acts Times CO changing Axe de Axe. Therefore, we have negative 20 caustic up, 30 degrees could tangent 30 degrees and then the possible error was remember it was plus or minus pi over 1 80 which simplifies to plus or minus 1.209 centimeters. Therefore, we have de age equals pulsar minus 1.209 centimeters, divided by 20 caustic it 30 degrees. That's 20 times two, which is 0.3 right. This is a percentage this is plus or minus 3%.

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