A tree is supported a wire anchored in the ground 11 feet from its base. The wire is 2 feet longer than the height that it reaches on the tree. Find the length on the wire.

Question

wolf1728 · Answer

Here is a diagram

wolf1728 · Answer

Let's call the tree height x
the length of the wire (the hypotenuse) w
and the distance from the tree 'd' which is eleven feet.

So, going by the Pythagorean Theorem
w² = 11² + x²
we are told that w is 2 feet longer than tree height so
(x + 2)² = 121 + x²
x² + 4x + 4 = 121 +x²
4x = 117

x=29.25 (TREE HEIGHT)

Length of Wire = 31.25

Double Check 
31.25² = 29.25² + 11²
976.5625 = 855.5625 + 121
976.5625 = 976.5625