# In order to estimate the height h of a tall pine tree, a student places a mirror on the ground...

## Question:

In order to estimate the height h of a tall pine tree, a student places a mirror on the ground and stands where she can see the top of the tree, as shown. The student is 6 feet tall and stands 3 feet from the mirror which is 11 feet from the base of the tree. What is the height h (in feet) of the pine tree?

## Plane Mirror:

A plane mirror is any flat reflective surface. It follows the law of reflection, where the angle of incidence is equal to the angle of reflection aas measured from a line perpendicular to the surface of the mirror.

## Answer and Explanation:

The student stands 3 feet from the mirror and 6 feet tall, while the tree is 11 feet from the base of the tree. Using the ratio of the height of the boy and distance from the mirror a proportion can be made to determine the height of the tree, such that:

{eq}\begin{align} \rm \dfrac{x \ height \ of \ tree }{11 \ feet } &= \rm \dfrac{6 \ feet \ height \ of \ student}{3 \ feet} \\ \dfrac x {11} &= \dfrac 6 3 \\ \dfrac x {11} &= 2 \\ x &= (2)(11) \\ x & = 22 \end{align} {/eq}

The tree is {eq}\rm 22 \ feet {/eq} high.

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from Geometry: High School

Chapter 7 / Lesson 1