Question

A carpenter building a shed roof places a strut from C to D, as shown, and it divides the roof asshown. How long is BC?

Answer 1

$\begin{gathered} AC^2+BC^2=(28.8+5)^2 \\ AC^2+BC^2=33.8^2 \\ \\ BC^2=5^2+DC^2 \\ \\ AC^2=28.8^2+DC^2 \end{gathered}$

We have created a set of equations to solve the problem

$\begin{gathered} 28.8^2+DC^2+5^2+DC^2=33.8^2 \\ \\ 2DC^2=33.8^2-28.8^2-5^2 \\ 2DC^2=288 \\ DC^2=\frac{288}{2} \\ DC^2=144 \\ DC=12 \end{gathered}$

Now with the DC value we can calculate the length of BC

$\begin{gathered} BC^2=5^2+DC^2 \\ BC^2=5^2+12^2 \\ BC=\sqrt[]{25+144} \\ BC=\sqrt[]{169} \\ BC=13 \end{gathered}$

The long of BC is 13