Question

A lighthouse has a shadow that is
feet long.
Zara is
feet tall, and has a shadow that is
feet long.
The two triangles formed are similar because the angle to the sun is the same.

Use this information to complete the statement about the lighthouse.


A right triangle with height of lighthouse question mark and width 36 feet. A right triangle with height of woman 4 feet and width 3 feet.

Answer 1

To solve the problem, we can use the concept of similar triangles. Since the triangles formed by the lighthouse and Zara are similar, the ratios of their corresponding sides are equal.

Let's denote:
- The height of the lighthouse as \( H \) feet.
- The height of Zara as 4 feet.
- The length of the lighthouse's shadow as \( S_L \) feet.
- The length of Zara's shadow as \( S_Z \) feet.

The relationship between the heights and shadows of the two triangles can be expressed as:

\[
\frac{H}{S_L} = \frac{4}{3}
\]

From this ratio, we can rearrange it to find the height of the lighthouse:

\[
H = \frac{4}{3} \times S_L
\]

If you provide the lengths of the shadows for both the lighthouse and Zara, we can calculate the exact height of the lighthouse.