Final answer:
The angle the boat's line of sight makes with Pier A relative to the shoreline is 45°. The angle the boat's line of sight makes with Pier B relative to the shoreline cannot be determined without more information. The distance between Pier A and Pier B cannot be determined without more information.
Step-by-step explanation:
To find the angle the boat's line of sight makes with Pier A relative to the shoreline, we can use the concept of trigonometry. Let's call this angle θ. We have the opposite side, which is the distance from the boat to Pier A (200 feet), and the adjacent side, which is the distance from the boat to the shoreline (also 200 feet). Using the tangent function, we can find θ by dividing the opposite side by the adjacent side: tan(θ) = opposite/adjacent = 200/200 = 1. Taking the inverse tangent of 1, we find that θ is 45°.
To find the angle the boat's line of sight makes with Pier B relative to the shoreline, we can use the same concept. Let's call this angle α. We have the opposite side, which is the distance from the boat to Pier B (which we don't know yet), and the adjacent side, which is still the distance from the boat to the shoreline (200 feet). Again, using the tangent function, we can find α by dividing the opposite side by the adjacent side: tan(α) = opposite/adjacent = PierB/200. Unfortunately, we don't have enough information to determine the exact value of α, so the answer is Cannot be determined.
To find the distance between Pier A and Pier B, we can use the concept of Pythagorean theorem. Let's call the distance from the boat to Pier B x. We can form a right triangle with sides 200 feet, x, and the distance between Pier A and Pier B. Using Pythagorean theorem, we have 200^2 + x^2 = (distance between Pier A and Pier B)^2. Since we don't know x or the distance between Pier A and Pier B, we cannot solve for the distance between Pier A and Pier B. Therefore, the answer is also Cannot be determined.