Math-Distance question?

Question

A family was watching the fireworks. The little girl said, "wow we are really lucky that our view isn't blocked-the bottoms of most of the fireworks appear right at the top of that 50 foot oak tree." The little girl is 100 feet from the oak tree and 1500 feet away from the fireworks launch site, how many feet off the ground were the bottoms of MOST of the fireworks?

Answer 1

750

Answer 2

50/100 = x/1500

x=750 feet

the distance from the girl to the bottom of the tree , the height of the tree, and from the girl to the top of the tree form a right triangle. The distance from the girl to the launch point of the fireworks forms one leg of a congruent and therefore proportional triangle.

Answer 3

A proportion will do here.  If Th and Td are the height and distance of the tree, and Fh and Fd are the height and distance of the fireworks, then we have Th/Td = Fh/Fd, and are given Th = 50, Td = 100, Fd = 1500, and Fh is to be found.  Simple arithmetic.