Answer:
274.8 feet
Explanation:
The diagram illustrating this problem is attached below:
The distance between the boat and the bottom of the lighthouse = x
Using trigonometric ratio:
[tex]\tan 27\degree=\frac{140}{x}[/tex]Cross multiply:
[tex]x\tan 27\degree=140[/tex]Divide both sides by tan 27.
[tex]\begin{gathered} \frac{x\tan 27\degree}{\tan 27\degree}=\frac{140}{\tan 27\degree} \\ x=274.77 \\ x\approx274.8ft \end{gathered}[/tex]The horizontal distance between the boat and the bottom of the light house is 274.8 feet (correct to the nearest tenth)
