PROBLEM:
A surveyor, standing 30 ft from the base of a building, measures the angle of elevation to the top of the building to be 75 degrees. How accurately must the angle be measured for the percentage error in estimating the height of the building to be less than 4%?
ATTEMPT:
I'm not really sure how to approach this problem. The condition requires that the estimation and the true value be less than 4%; or,
where df and f(x) represents the height of the building and its differential is a result of the propagation of error in measuring the angle of elevation.