(Solved): On a day when the sun passes directly overhead at noon, a 6-ft-tall man casts a shadow of length 6 s ...

On a day when the sun passes directly overhead at noon, a 6- $\mathrm{ft}$-tall man casts a shadow of length $S(t)=\frac{6}{?\tan \left(\frac{?}{12}t\right)?}$ 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 7:00 A.M., noon, and 2:00 P.M. (Round your answers to (b) Sketch a graph of the function $s$ for $0<t<12$. 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 (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 values correspond? $t=6$; that is, at noon $t=1$ and $t=11$; that is, at 11:00 A.M. and 1:00 P.M $t=1$ and $t=11;$ that is, at 7:00 A.M. and 5:00 P.M $t=3$ and $t=9;$ that is, at 3:00 A.M. and 9:00 P.M $t=3$ and $t=9;$ that is, at 9:00 A.M. and 3:00 P.M (d) Explain what happens to the shadow as the time approaches 6 P.M. (that is, as $t?12^{?}$). The shadow gets increasingly longer. The length of the shadow approaches 6 feet. The length of the shadow approaches 12 feet. The length of the shadow approaches 46 feet. The shadow gets increasingly shorter.