Thread: Some difficult written task

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. How accurately must the angle be measured for the
percentage error in estimating the height of the building to be less than 4%?

I am not sure where to even start on this.

Start by expressing h as a function of the angle α: h = h(α). Let Δh = 0.04 ⋅ h(75°). We have approximately Δh = h'(75°) ⋅ Δα, from where we can find Δα.