Surveying a bluff A surveyor, using a transit, sights the edge B of a bluff, as shown in t...

Surveying a bluff A surveyor, using a transit, sights the edge B of a bluff, as shown in the left part of the figure (not drawn to scale). Because of the curvature of Earth, the true elevation h of the bluff is larger than that measured by the surveyor. A cross-sectional schematic view of Earth is shown in the right part of the figure.

(a) If s is the length of arc PQ and R is the distance from P to the center C of Earth, express h in terms of R and s.

(b) If R = 4000 mi and s = 50 mi, estimate the elevation of the bluff in feet.

EXERCISE