posted by Dan .
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 24-foot shadow.
Let T be the tree top
Let B be the tree base
Let S be the tip of the shadow
tan(angle BST) = 34/24
angle BST = 54.78°
This is also the angle of the sun from the horizon
54.78/90 = .61
so, the sun has gone .61* 6 hours = 3.66 hrs = 3 hr 40 min, so the time is 9:40 am.
Of course, the shadow is the same length at 2:20 pm, assuming no cloud cover...