Question

A ladder that is 10 yards in length is resting on a branch of a tree, and the base of the ladder is 6 yards from the tree on the level ground. How high up is the branch on which the ladder is resting?

Answer 1

Given the information, we can make a simple picture to see what we need to measure:

Now, using the pythagorean theorem, we have:

$c^2=a^2+b^2$

In this case, we have that c^2=10 and b^2=6, then we need to solve for a:

$\begin{gathered} c^2=a^2+b^2 \\ \Rightarrow a^2=c^2-b^2 \\ \Rightarrow a^2=(10)^2-(6)^2=100-36=64 \\ \Rightarrow a^2=64 \\ \Rightarrow a=\sqrt[]{64}=8 \\ a=8 \end{gathered}$

Therefore, the branch is 8 yards high.