Answer
$30\frac{1}{8}$ ft.
Work Step by Step
The tree and the segment connecting the base of the tree to the point on the ground where the wire is anchored are the legs of a right triangle, while the wire is its hypotenuse. Let's note the height of the tree by $x$. The distance on the ground between the base of the tree and the point where the wire is anchored is $15$ feet. The hypotenuse is $x+4$ feet.
Apply the Pythagorean Theorem.
$hypotenuse^2=leg_1^2+leg_2^2$
$\Rightarrow (x+4)^2=x^2+15^2$
Square $(x+4)$ and $15$.
$\Rightarrow x^2+8x+16=x^2+225$
Subtract $x^2+16$ from both sides.
$\Rightarrow x^2+8x+16-x^2-16=x^2+225-x^2-16$
Simplify.
$\Rightarrow 8x=209 $
Divide both sides by $8$.
$\Rightarrow \frac{8x}{8}=\frac{209}{8} $
Simplify.
$\Rightarrow x=\frac{209}{8} $
Length of the wire is
$=x+4$
$=\frac{209}{8}+4$
$=\frac{209+32}{8}$
$=\frac{241}{8}$
$=30\frac{1}{8}$ ft.
