If a surveyor measures differences in elevation when making plans for a highway across a desert, corrections must be made for the curvature of the earth.
(a) If R is the radius of the earth and L is the length of the highway, show that the correction is
C = R sec (L/R) - R
(b) Use a Taylor polynomial to show that

(c) Compare the corrections given by the formulas in parts (a) and (b) for a highway that 100 km long. (Take the radius of the earth of be 6370 km.)

2R 24R