Question

A grain silo casts a shadow of 40 feet while a nearby fence post casts a shadow of 2 feet. The fence post is 5.8 feet high. How tall is the grain silo?

Answer 1

To find the height of the grain silo, we can use the concept of similar triangles. The ratios of the height of an object to the length of its shadow will be the same for both the grain silo and the fence post.

Let \( h \) be the height of the grain silo. According to the provided information:

- Height of fence post: \( 5.8 \) feet
- Shadow of fence post: \( 2 \) feet
- Shadow of grain silo: \( 40 \) feet

We can set up a proportion:

\[
\frac{\text{Height of fence post}}{\text{Shadow of fence post}} = \frac{\text{Height of grain silo}}{\text{Shadow of grain silo}}
\]

Substituting the known values:

\[
\frac{5.8}{2} = \frac{h}{40}
\]

Now, we can cross-multiply to solve for \( h \):

\[
5.8 \times 40 = 2 \times h
\]

Calculating \( 5.8 \times 40 \):

\[
5.8 \times 40 = 232
\]

So, we have:

\[
232 = 2h
\]

Now, divide both sides by \( 2 \) to find \( h \):

\[
h = \frac{232}{2} = 116
\]

Thus, the height of the grain silo is \( \boxed{116} \) feet.