Solution:
Given:
Description of a person's view from a lighthouse to a boat.
This can be sketched as shown below;
The sketch can be made as a right triangle;
To get the distance between the boat and the lighthouse, we use the trigonometrical ratio of tangent.
[tex]\begin{gathered} \tan \theta=\frac{\text{opposite}}{adjacent} \\ \text{where;} \\ \theta=28^0 \\ \text{opposite=200} \\ \text{adjacent}=x \end{gathered}[/tex]
Hence,
[tex]\begin{gathered} \tan \theta=\frac{\text{opposite}}{adjacent} \\ \tan 28=\frac{200}{x} \\ \text{Cross multiplying;} \\ x\times\tan 28=200 \\ x=\frac{200}{\tan 28} \\ x=376.15 \\ To\text{ the nearest foot,} \\ x\approx376ft \end{gathered}[/tex]
Therefore, to the nearest foot, the lighthouse is 376 feet away from the lighthouse.
