Final answer:
To calculate the angles, we can use trigonometry. The angle the line of sight makes with pier A relative to the shoreline is arctan(200/distance between pier A and the shore). The angle the line of sight makes with pier B relative to the shoreline is arctan(200/distance between pier A and the shore). The distance between pier A and pier B can be found using the Law of Cosines.
Step-by-step explanation:
To calculate the angles, we can use trigonometry. Let's call the angle the line of sight makes with pier A relative to the shoreline as angle A, and the angle the line of sight makes with pier B relative to the shoreline as angle B.
We are given the distance between the boat and the shore, which is 200 feet. We can use this information to form a right triangle between the boat, pier A, and the shoreline. The opposite side of the triangle is the distance between the boat and pier A, which is 200 feet.
The adjacent side is the distance between pier A and the shore, which is the same as the distance between pier A and pier B. To find the angle A, we can use the inverse tangent function: angle A = arctan(opposite/adjacent) = arctan(200/distance between pier A and the shore).
Similarly, we can form a right triangle between the boat, pier B, and the shoreline. In this triangle, the opposite side is the distance between the boat and pier B, which is also 200 feet. The adjacent side is still the distance between pier A and the shore, or the distance between pier A and pier B. To find the angle B, we can use the same formula: angle B = arctan(200/distance between pier A and the shore).
To calculate the distance between pier A and pier B, we can use the Law of Cosines. The formula is: c^2 = a^2 + b^2 - 2ab*cos(C), where c is the side opposite the angle C, and a and b are the other two sides. In our case, a and b are both the distance between pier A and the shore, so let's call it x.
The angle C is 180 degrees minus angle A and angle B, since the three angles in a triangle add up to 180 degrees.
Substituting these values into the formula, we get: distance between pier A and pier B = sqrt(x^2 + x^2 - 2x*x*cos(180 - angle A - angle B)).
Learn more about Angles in Triangles