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Answer :
Final answer:
By using the Pythagorean theorem, it can be determined that at high tide, the boat is approximately 27.8 feet above the seafloor.
Explanation:
The situation described in this question can be solved using Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The anchor rope is the hypotenuse in this case.
At low tide, we can form a triangle, where the vertical distance from the boat to the seafloor is a = 20 ft (this is one leg of the triangle) and the horizontal distance from the boat to the anchor is b = 40 ft (this is the other leg of the triangle). So the length of the hypotenuse or the anchor rope, c, is given by sqrt(a^2 + b^2) = sqrt(20^2 + 40^2) = sqrt(400 + 1600) = sqrt(2000) = 44.72 ft. Even at high tide, the length of the hypotenuse or the anchor rope remains the same i.e., 44.72 ft.
At high tide again we can form a triangle with the anchor rope being the hypotenuse of 44.72 ft and horizontal distance as one leg of the triangle as 35 ft. Let's denote the vertical distance from the boat to the seafloor at high tide as x, which we need to find. So according to Pythagorean theorem, (44.72)^2 = (35)^2 + x^2. Solving for x gives approximately x = 27.8 ft.
Therefore, at high tide, the boat is approximately 27.8 ft above the seafloor. This corresponds to option a: 27.8 ft.
Learn more about Pythagorean theorem here:
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