Question

A person who is 6 feet tall casts a 3-foot long shadow.A nearly s pine tree casts 15-foot long shadow.What is the height h of the pine tree?

Answer 1

The length of the shadow is half of the actual object therefore double the length of the shadow would equal the length of the object.

6:3
s:15

15x2=s because, 3x2=6

Answer 2

For this case we can model the problem as two similar triangles.

The two triangles have a right angle.

For triangles we have the base of each triangle.

We have the height of one of the triangles (the smallest)

We want to determine the height of the largest triangle.

By similarity of triangles we have:

$\frac{h}{15} =\frac{6}{3}$

Rewriting we have:

$h = (\frac{6}{3}) (15)\\h = 30 feet$

Answer:

The height of the pine tree is:

$h = 30 feet$