Question

The bird house in your friend's yard casts a shadow that is 1414 feet long. Your friend is 55 feet tall and casts a shadow that is 3.53.5 feet long. What is the height of the bird house?

Answer 1

What kinds of numbers are these? Numbers don't have two decimals, and a shadow that is 1414 ft long is pretty long...

Either way the shadow that is cast is proportional to the length of the actual object.
So you have to set up a proportion

$\frac{birdhouseheight}{birdhouse shadow}$ = $\frac{yourfriendsheight}{friendsshadow}$

It doesn't matter, you could put it this way too:
$\frac{birdhouse shadow}{birdhouseheight}$ = $\frac{friends shadow}{your friends height}$

Plug in the known information:
$\frac{1414 ft}{x}$ = $\frac{3.53.5 ft}{55 ft}$

Solve for x = birdhouse ft