Answer
$13$ ft.
Work Step by Step
The tree and the distance from the base of the tree and the point where the wire is anchored on the ground are the legs of a right triangle. The wire is the hypotenuse.
Let $x$ be the height of the tree. The length of the other leg is $5$. The length of the hypotenuse, $x+1$, represents the length of the wire.
Apply the Pythagorean Theorem.
$hypotenuse^2=leg_1^2+leg_2^2$
$\Rightarrow (x+1)^2=x^2+5^2$
Square $(x+1)$ and $5$.
$\Rightarrow x^2+2x+1=x^2+25$
Subtract $x^2+1$ from both sides.
$\Rightarrow x^2+2x+1-x^2-1=x^2+25-x^2-1$
Simplify.
$\Rightarrow 2x=24 $
Divide both sides by $2$.
$\Rightarrow \frac{2x}{2}=\frac{24}{2} $
Simplify.
$\Rightarrow x=12$
The length of the wire is
$=x+1$
$=12+1$
$=13$ ft.
