Question

Irene places a mirror on the ground 24 feet from the base of an oak tree. She walks backward until she can see the top of the tree in the mirror. At that point, Irene's feet are 4 feet from the mirror. How tall is the oak tree?

Answer 1

$\begin{gathered} Irene´s\text{ high= }5.5\text{ ft} \\ Irene´s\text{ f}eet\text{ from the mirror= 4ft} \\ \theta_I=\theta_{II}=\theta \\ \text{From Irene´s triangle} \\ \tan \text{ }\theta=\frac{5.5}{4} \\ \\ From\text{ Oak´s triangle} \\ \tan \text{ }\theta=\frac{x}{24} \\ \\ \frac{5.5}{4}=\frac{x}{24} \\ \\ x=\frac{5.5}{4}\cdot24 \\ \\ x=\text{ 33} \\ The\text{ oak´s high is 33 ft} \end{gathered}$