Question

John has a 10-foot piece of rope that he wants to use to support his 8-foot tree. How far from the base of the tree should he secure the rope?

Short answer

Distance from tree's base to secure rope is 6 foot.

Step-by-step solution

Step 1. Given Information

Rope's length is 10 foot and tree's height is 8 foot.

Step 2. Pythagoras Theorem

On applying the data in the formula,

$$\begin{gathered} {\mathrm{Base}}^2+{\mathrm{height}}^2={\mathrm{Hypotenuse}}^2 \\ {\mathrm{x}}^2+8^2={10}^2 \\ {\mathrm{x}}^2+64=100 \\ {\mathrm{x}}^2=36 \\ \mathrm{x}=\sqrt{36} \\ \mathrm{x}=6 \end{gathered}$$

Distance from base of tree for securing rope is 6 foot.