Chapter 12.9, Problem 7P

Assuming that the earth is a perfectly round, smooth ball of radius 4000 miles and that 1 mile = 5280 feet, how far away does the horizon appear to be to a 5-foot-tall person on a clear day? Explain your reasoning. To solve this problem, start by making a math drawing that shows the cross-section of the earth, a person standing on the surface of the earth, and the straight line of the person's gaze reaching to the horizon. (Obviously, you won’t want to draw this to scale.) You will need to use the following geometric fact: If a line is tangent to a circle at a point P (meaning itjust “grazes” the circle at the point P; it meets the circle only at that one point), then that line is perpendicular to the line connecting P and the center of the circle, as illustrated in Figure 12.105

Figure 12.105 A line tangent to a circle.