The triangle formed is a right triangle, so we can relate angles and sides with trigonometric ratios.
We have to calculate the distance from the boat to the lighthouse.
This distance is the hypotenuse of the right triangle.
We can relate the hypotenuse H with the angle with measure 52° and its adyacent side A = 30 miles as:
[tex]\begin{gathered} \cos (52\degree)=\frac{A}{H} \\ H=\frac{A}{\cos (52\degree)} \\ H=\frac{30}{\cos (52\degree)} \end{gathered}[/tex]
Answer: the distance is 30/cos(52°) [Option D]
