Question

For a project in his Geometry class, Marques uses a mirror on the ground to measure the height of his school’s flagpole. He walks a distance of 13.85 meters from the flagpole, then places a mirror flat on the ground, marked with an X at the center. He then walks 2.1 more meters past the mirror, so that when he turns around and looks down at the mirror, he can see the top of the flagpole clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.65 meters. How tall is the flagpole? Round your answer to the nearest hundredth of a meter.

Answer 1

Step-by-step explanation

We will represent the given parameters in the image below.

Using similar triangles, we can find the height of the flagpole.

`(h)/(13.85)=(1.65)/(2.1)`

We will then cross multiply and solve for x.

`\begin{gathered} 2.1* h=13.85*1.65 \\ h=(13.85*1.65)/(2.1) \\ h=10.88 \end{gathered}`

Answer: 10.88 meters