Question

.
A 6 foot tall man makes a shadow that is 3 1/2 feet long. How tall is a building that makes a 14 7/8
foot shadow?

25.5 feet

1.41 feet

8.68 feet

52.06 feet

Answer 1

To find the height of the building based on the ratio of the heights and the lengths of the shadows, we can use similar triangles.

Let:
- \( h_m \) = height of the man = 6 feet
- \( s_m \) = length of the man's shadow = 3.5 feet
- \( h_b \) = height of the building (unknown)
- \( s_b \) = length of the building's shadow = 14.875 feet

From the property of similar triangles, we have:

\[
\frac{h_m}{s_m} = \frac{h_b}{s_b}
\]

Substituting the known values into the equation:

\[
\frac{6}{3.5} = \frac{h_b}{14.875}
\]

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

\[
6 \times 14.875 = 3.5 \times h_b
\]

Calculating the left side:

\[
6 \times 14.875 = 89.25
\]

Now we have:

\[
89.25 = 3.5 \times h_b
\]

To find \( h_b \), divide both sides by 3.5:

\[
h_b = \frac{89.25}{3.5}
\]

Calculating this:

\[
h_b = 25.5 \text{ feet}
\]

Thus, the height of the building is **25.5 feet**.