Question
Asked Mar 24, 2020
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You measure the angle from the ground to the top of the building from a point 70 feet away from the base of the building. The true value of the angle is 60 degrees, but your measurement may be in error by as much as ±2∘. Assuming level ground and a plumb building, use differentials to approximate the maximum possible error in calculating the height of the building using your measurement of the angle. Round your answer to three decimal places.

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Expert Answer

Step 1

Given:

Base, x=70 ft

Calculus homework question answer, step 1, image 1

Let height of the building = h

A rough sketch of the given problem is as follows:

Calculus homework question answer, step 1, image 2

Step 2

In the above triangle:

Calculus homework question answer, step 2, image 1

Error in h is given as:

Calculus homework question answer, step 2, image 2

Calculus homework question answer, step 2, image 3

Step 3

Calculus homework question answer, step 3, image 1

We get:

Calculus homework question answer, step 3, image 2

 

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