# calculus

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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.

• calculus -

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...

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