To solve the problem, we can model the situation as a triangle where we know the distance between the two docks and the bearings from each dock to the coral reef. The Law of Sines can then be applied to find the distance from dock A to the coral reef.

Here’s the breakdown of the information provided:

1. The two docks are 2583 ft apart (the distance between dock A and dock B).
2. The bearing from dock A to the coral reef is $60^\circ 27'$, which can be converted to $60.45^\circ$.
3. The bearing from dock B to the coral reef is $330^\circ 27'$. Since bearings are measured clockwise from the north, the angle from dock B relative to the east-west line is $360^\circ - 330^\circ 27' = 29^\circ 33'$, which converts to $29.55^\circ$.

Next, we calculate the interior angles of the triangle:

• The angle at dock A is $60.45^\circ$.
• The angle at dock B is $180^\circ - 29.55^\circ = 150.45^\circ$.
• The angle at the coral reef (let's call it $C$) can be found by subtracting the angles at A and B from 180 degrees: $C = 180^\circ - 60.45^\circ - 29.55^\circ = 90^\circ.$

We now have a right triangle, which simplifies the calculation.

Since $C = 90^\circ$, we can use basic trigonometry or the Law of Sines. However, the most straightforward approach would be to apply basic trigonometric functions like the sine or cosine law since it's a right triangle.

Let's proceed with these steps and calculate the distance from dock A to the coral reef.The distance from dock A to the coral reef is approximately 1464 feet, rounded to the nearest integer.

Would you like further details on how this was calculated or have any other questions? Here are 5 related questions you might find useful:

1. How do you calculate bearings and convert them into angles for trigonometric use?
2. What is the Law of Sines, and how does it work in non-right triangles?
3. Can the Law of Cosines be used in this problem? If so, how?
4. How do you convert angles given in degrees and minutes into decimal degrees?
5. How does the right-triangle assumption simplify solving problems with bearings?

Tip: When working with bearings, always pay attention to whether they are measured clockwise or counterclockwise, as this can affect the angle calculations in trigonometry.