geometry question

Question

a 24-foot flagpole casts a 20-foot shadow. at the same time, the building next to it casts an 85-foot shadow. find the height of the building?

Answer 1

Hi Roseann,

For this question, I find it easiest to set up a ratio. You should assume that the height of the building and it's shadow should be proportional to the height of the flagpole and its shadow, which is what allows you to create this ratio. Let's label the height of the building (what we are trying to find) as h. Therefore, our ratio should be set up as:

flagpole shadow / flagpole height = building shadow / building height

20 ft / 24 ft = 85 ft / h ft

Now, let's solve this equation to find the value of h.

h(20/24) = h(85/h)

24(20h/24) = 24(85)

(1/20)*20h = (1/20)*2040

h = 102 feet

The height of the building is 102 feet!