PROBLEM
integer problem
a christmas tree is supported by a wire that is 1 foot longer than the height of the tree. The wire is anchored at a point whose distance from the base of the tree is 49 feet shorter than the height of the tree. what is the height of the tree?
a christmas tree is supported by a wire that is 1 foot longer than the height of the tree. The wire is anchored at a point whose distance from the base of the tree is 49 feet shorter than the height of the tree. what is the height of the tree?
|\
| \ LENGTH OF
HEIGHT OF | \ SUPPORT
TREE, h | \ WIRE, h + 1
| \
|___\
h - 49
SUPPORT WIRE ANCHOR
USE PYTHAGOREAN THEOREM
(h + 1)^2 = h^2 + (h - 49)^2
h^2 + 2h + 1 = h^2 + h^2 - 98h + 2401
Simplifying...
h^2 - 100h + 2400 = 0
Factoring...
(h - 60)(h - 40) = 0
h - 60 = 0, h - 40 = 0
h = 60, h = 40
Since the wire is anchored a distance 49 feet shorter than the height of the tree, h = 40 is not valid.
Therefore, the height of the tree, h, is 60 feet.
