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# How accurate must an angle measurement be for error in height estimation to be less than 9%?

A surveyor standing 50 feet from the base of a large tree measures the angle as 71.5°. How accurately must the angle be measured if the percent error in estimating the height of the tree is to be less than 9%? (Give your answer correct to 3 decimal places.)

I got .018, which is apparently wrong.

### 1 Answer

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- KeithLv 710 years agoBest Answer
tan (71.5) = H / 50

H = 50 * tan(71.5) = 149.43425

149.43425 + 9% = 162.88333

149.43425 - 9% = 135.98517

tan (x) = 162.88333 / 50

x = 72.9352

tan (x) = 135.98517 / 50

x = 69.8122

72.9352 - 71.5 = 1.435 degrees

71.5 - 69.8122 = 1.688 degrees

The smaller error is 1.435 degrees

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