On a day when the sun passes directly overhead at noon, a 1.80-m-tall man casts a shadow of length S(t)=1.8|cot(πt/12)|, where S is the length of shadow in meters and t is the number of hours since 6am, at what time from the following list the length of the shadow would equal to the man’s height?

Question

On a day when the sun passes directly overhead at noon, a 1.80-m-tall man casts a shadow of length S(t)=1.8|cot(πt/12)|, where S is the length of shadow in meters and t is the number of hours since 6am, at what time from the following list the length of the shadow would equal to the man’s height?
(A) 3pm (B) 4pm (C) 5pm (D) 6pm (E) never happen

oobleck · Answer

clearly, when cot(πt/12) = 1 πt/12 = π/4 t = 3 Huh. I get 9am Note that at noon, t=6, and the shadow has zero length.

AJ L · Answer

For the length of the shadow to be equal to the man's height, then S(t)=1.8, meaning the equation becomes:
1.8=1.8|cot(πt/12)|
1=|cot(πt/12)|
1=1/tan(πt/12)
tan(πt/12)=1
πt/12=π/4
πt=3π
t=3

This means 3 hours after 6am would be 9am, which means none of the times on the list are correct, making option E correct.