Answer:
The little brother should place the mirror at 36 ft from the base of the tree to properly see its top
Step-by-step explanation:
Similar Triangles
Two triangles are defined as similar if their corresponding angles are congruent and the corresponding sides are in proportion. The triangle formed by the kid and the ground and the triangle formed by the tree and the ground are similar since the angle of reflection over the mirror is the same, i.e. the light travels in a straight line. This means that we can set this proportion
[tex]\displaystyle \frac{x}{72}=\frac{2}{4}[/tex]
Solving for x
[tex]\displaystyle x=\frac{2\times 72}{4}[/tex]
[tex]\boxed{x=36\ ft}[/tex]
The little brother should place the mirror at 36 ft from the base of the tree to properly see its top
