Question

The bird house in your friend's yard casts a shadow that is 14 feet long. Your friend is 5 feet tall and casts a shadow that is 3.5 feet long. What is the height of the bird house?

Answer 1

20 feet high

Explanation:

Do the work

Answer 2

Bird house is 20 ft. high.

Explanation:

Let the height of the bird house is h feet high casts a shadow of 14 ft long.

My friend is 5 feet high and casts a shadow of 3.5 feet.

Now we see both the triangles Δ ABC and Δ XYZ are similar.

By the similar triangles theorem sides opposite to the corresponding angles will be in the same ratio.

`(5)/(h)=(3.5)/(14)` (from similar triangles ABC and XYZ)

`h=(14*5)/(3.5)=(70)/(3.5)=20 ft.`

Therefore bird's house is 20 feet high.