Chapter 1, Problem 39P

The height of a building may be estimated by measuring the horizontal distance to a point on the ground and the angle from this point to the top of the building. Assuming these measurements are L = 100 ± 0.5 ft and θ = 30 ± 0.2°, estimate the height H of the building and the uncertainty in the estimate. For the same building height and measurement uncertainties, use Excel's Solver to determine the angle (and the corresponding distance from the building) at which measurements should be made to minimize the uncertainty in estimated height. Evaluate and plot the optimum measurement angle as a function of building height for 50 ≤ H ≤ 1000 ft.