Let's denote the length of the shadow cast by the lighthouse as "x". We can set up a proportion to solve for x.
Since Carley's height is 5 feet and her shadow is 3.8 feet, we have:
$$\frac{x}{205} = \frac{3.8}{5}$$
To find x, we cross-multiply and solve for x:
$$5x = 205 \times \frac{3.8}{5}$$
Simplifying the right side:
$$5x = 41.1$$
Finally, dividing both sides by 5:
$$x = \frac{41.1}{5}$$
Therefore, the length of the shadow cast by the lighthouse is $$x = 8.22$$ feet.
