Question

Micah places a mirror on the ground 24 feet from the base of a tree. He walks

Answer 1

The height of tree is 8 feet

Solution:

Given, Micah places a mirror on the ground 24 feet from the base of a tree

At that point, Micah's eyes are 6 feet above the ground  

And he is 9 feet from the image in the mirror.  

To find : height of tree = ?

Let "n" be the height of tree

From the question, we can see there is a directly proportional relationship between heights and distances.

Proportional relationships are relationships between two variables where their ratios are equivalent.

$\frac{\text { height of micah eyes above ground }}{\text { distance of micah from mirror }}=\frac{\text { height of tree above the ground }}{\text { distance of tree from mirror }}$

$\begin{array}{l}{\frac{6 \text { feet }}{9 \text { feet }}=\frac{n \text { feet }}{24 \text { feet }}} \\\\ {\frac{6}{9}=\frac{n}{24}} \\\\ {\text { n }=\frac{1}{3} \times 24} \\\\ {\text { n }=8}\end{array}$

Hence, the height of the tree is 8 feet