Which triangles are similar?
The triangle AED and the triangle ABC is similar.
How do you know?
Because all the angles are equal, the triangle AED and ABC have the same angle values, then they're similar.
Find the height of the tree (This distance from B to C)
We can use the relation of the similar triangle to find BC, we can write the equation
[tex]\frac{AB}{AD}=\frac{BC}{ED}[/tex]
The only unknown value here is BC, then
[tex]\frac{24+8}{8}=\frac{\text{BC}}{5}[/tex]
Now we solve it for BC!
[tex]\begin{gathered} \frac{32}{8}=\frac{BC}{5} \\ \\ 4=\frac{BC}{5} \\ \\ BC=4\cdot5 \\ \\ BC=20\text{ ft} \end{gathered}[/tex]
Hence, the height of the tree is 20 ft
