Hello, sinjid9!

To find the height of a tree, Sarah placed a mirror on the ground 15 m from the base of a tree.

She walked backward until she could see the top of the tree in the centre of the mirror.

At that position she was 1.2m from the mirror and her eyes were 1.4m from the ground. Code:

o C
* |
* |
* |
A o * | h
| * * |
1.4 | * * |
| θ * * θ |
B o - - - o - - - - - - - o D
1.2 M 15

Sarah is $\displaystyle AB = 1.4 $

The tree is $\displaystyle CD = h.$

The mirror is at $\displaystyle M\!:\;\;BM = 1.2,\;MD = 15$

Since "angle of reflection equals angle of incidence",

. . we have: .$\displaystyle \angle AMB \,=\,\angle CMD \,=\,\theta.$

Hence: .$\displaystyle \Delta CDM \sim \Delta ABM$

Therefore: . $\displaystyle \frac{h}{15} \;=\;\frac{1.4}{1.2} \quad\hdots\;\text{etc.} $