Question

A 3-foot pole casts a 4-foot shadow at a particular time of day. If a nearby tree casts a shadow 15 feet long at the same time of day, how tall is the tree?

Enter the exact value of your answer; do not round!

Answer 1

The tree is 11.25 feet tall.

Explanation:

Please see the image attached as well. Sorry for the bad handwriting, I'm on a computer.

We can think of this problem as two similar triangles, with the shadows and the objects forming that triangle.

To solve the height of similar triangles, we will set up a proportion.

3/4=x/15

You can also set up the proportion like this:

4/3=15/x

Either way, it doesn't really matter. I'm going to use 3/4=x/15.

Now we can use cross products to find our answer.

3×15=4x

45=4x

x=11.25

Therefore, the tree is 11.25 feet tall. Hope this helps!