Question

A surveyor, standing 100 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%?

Answer 1

Right well Height = 100tan75
=373.205ft

if we say that the angle of elevation is 'a' = 75 degrees
so dH/da=100sec^2(a)

and then from that we can say that:
the fractional change in height is = dH/H = 0.04( for 4%)

hence 0.04 = 100sec^2(a)da/H, where da is the change in angle
and so da = 0.04H/(100sec^2(a))
da = 0.01

That's my take anyway