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what is the height of a tree, if a person 5ft. is 108ft from the base

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a person who is five feet tall is standing 108 ft, from the base of a tree, and the tree casts a 120 foot shadow. The persons shadow is 12 feet in length. What is the height of the tree?

asked Mar 1, 2014 in GEOMETRY by andrew Scholar

1 Answer

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Let x = height of the tree

From the diagram ABC and DEC are similar triangles(one inside the other).

From properties of similar triangle corresponding sides are all in the same proportion.

AB/DE = BC/EC

The ratio is  x/5 = 120/12

x/5 = 10

x = 50

Height of the tree is 50 ft.

answered Apr 26, 2014 by david Expert

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