Question

If the sun rises at 6 AM and is directly overhead at 12 noon, estimate the time (hour and
minutes) when a 34-foot tree will have a 14-foot shadow.

Answer 1

At the point in time when the tree shadow is 14 feet in length, a light ray joining the top of the tree to that end of the shadow that is away from the base of the tree, makes an angle of
\[\theta=\tan^{-1} {(14/34)} \]
The following expression evaluates to the time day, AM, that the shadow will be 14 feet in length.
\[12-{\theta \over ( \pi/2)}*6 = 10.508\]
or 10:30 AM