Your friend is trying to calculate the height of a nearby oak tree. You tell him that you learned how to use similar triangles in Geometry class. You tell your friend to measure his height (75 inches) and you measure the length of his shadow (48 inches). Both of you measure the length of the tree’s shadow (38 feet). How tall is the tree (in feet)? Round to the nearest hundredth.

Question

anonymous · Answer

Your friend's feet, his head, and the end of his shadow form a triangle.
The tree's lower trunk end, its top, and the end of its shadow form another triangle.
Since the angle between the ground and your friend is the same as the angle between the tree and your friend (roughly 90 degrees), and the sun has the same angle overhead for both your friend and the tree, the two are similar triangles.
That means the ratio of your friend's height to the length his shadow must be the same as the ratio of the tree's height to the length of its shadow:

75"/48" = h/456"

(38ft = 456")
Solve for h, and there you have it :)

anonymous · Answer

That was supposed to say 'the angle between the ground and your friend is the same as the angle between the ground and the tree'.

It's late.

anonymous · Answer

Oh, and of course the result will be in ", so you'll have to convert back to feet.