Answer:
[tex]611\:\text{ft}[/tex]
Step-by-step explanation:
In a right triangle only, the tangent of an angle is equal to its opposite side divided by its adjacent side. In this angle marked as [tex]42^{\circ}[/tex] is actually the same as the angle with point [tex]P[/tex].
Therefore, we can set up the following equation:
[tex]\tan 42^{\circ}=\frac{550}{x}[/tex], where [tex]x[/tex] is the distance from the coast.
Solving, we get:
[tex]x=\frac{550}{\tan 42^{\circ}},\\x\approx610.84\approx \boxed{611\:\text{ft}}[/tex]
