Question: 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

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 ≈ L2/2R + 5L4/24R3
(c) Compare the corrections given by the formulas in parts (a) and (b) for a highway that is 100 km long. (Take the radius of Earth to be 6370 km.)

1C R.

1C R.

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