solve the following problem using the properties of similar triangles. a 40 foot flagpole outside an office building casts a 25 foot shadow what is the height of the office building if the shadow is 200 feet long

Answer 1

Let the height of the office building be $h$ feet.

According to the given information, the flagpole is 40 feet tall and casts a shadow that is 25 feet long, and the office building casts a shadow that is 200 feet long.

We can form a proportion using the heights and shadows of the flagpole and office building:

$\frac{40}{25} = \frac{h}{200}$

Solving for $h$:

$40 \times 200 = 25h$

$8000 = 25h$

$h = \frac{8000}{25}$

$h = 320$

Therefore, the height of the office building is 320 feet.