Chapter 1.15, Problem 33P

If you are at the top Of a tower Of height h above the surface of the earth, show that the distance you can see along the surface of the earth is approximately $s=\sqrt{2Rh}$, where R is the radius of the earth. Hints: See figure. Show that $h/R=\sec \theta -1$; find two terms Of the series for $\sec \theta =1/\cos \theta$

Use $s=R\theta$.

Thus show that the distance in miles is approximately $\sqrt{3h/2}$ with h in feet.