Chapter 6.4, Problem 62E

Length of a Shadow On a day when the sun passes directly overhead at noon, a 6–ft–tall man casts a shadow of length

$S(t)=6\left|\cot \frac{\pi }{12}t\right|$

where S is measured in feet and t is the number of hours since 6 A.M.

(a) Find the length of the shadow at 8:00 A.M., noon, 2:00 P.M. and 5:45 P.M.

(b) Sketch a graph of the function S for 0 < t < 12.

(c) From the graph, determine the values of t at which the length of the shadow equals the man’s height. To what time of day does each of these value corresponds?

(d) Explain what happens to the shadow as the time approaches 6 P.M. (that is $t\to {12}^{-}$ ).