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

Question

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?

Answer 1

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.