# If a flagpole 12 feet tall casts a shadow that is 16 feet long, find the length of the shadow...

## Question:

If a flagpole 12 feet tall casts a shadow that is 16 feet long, find the length of the shadow cast by an antenna which is 18 feet tall. The angle of elevation of the sun is the same for the shadows.

## Flagpole Finial:

A flagpole has a decorative element at the very top called a finial. More often tha not it is in the shape of a ball or a combination of a ball and a pointed structure. It is sometimes called a hip-knob.

The flagpole that is 12 feet tall casta a 16-foot long shadow. If the antenna casts an 18 feet tall shadow, the height of it can be determined by using the information to make a proportion and solve for the height, {eq}x {/eq}:

{eq}\begin{align} \rm \dfrac {x \ feet \ antenna}{18 \ feet \ shadow} &= \rm \dfrac {12 \ feet \ flagpole }{ 16 \ feet \ shadow} \\ \dfrac x {18} &= \dfrac {12}{16} \\ x &= \dfrac {(12)(18)}{16} \\ x &= \dfrac {(4)(3)(9)(2)}{(4)(2)(2)} \\ x &= \dfrac {27} 2 \\ x &= 13 \dfrac 1 2 \end{align} {/eq}

The antenna is {eq}\rm 13 \dfrac 1 2 \ feet {/eq} high. 