A rope is connected to a boat and to the boat's anchor that is resting on the ocean floor at a position not directly under the boat. The rope is 105 feet long and the water is 55 feet deep. To the nearest tenth of a foot, how far is the anchor from a point directly below the point?
To find the distance between the anchor and the point directly below the boat, we can use the Pythagorean theorem.
Let's denote the distance between the anchor and the point directly below as 'x'. We know that the water is 55 feet deep, so we can denote the length of the rope from the boat to the anchor (along with the vertical distance in the water) as '105 - 55 = 50'.
According to the Pythagorean theorem, the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In our case, the length of the rope is the hypotenuse, and the vertical distance in the water is one of the legs. So we have:
x^2 + 55^2 = 50^2
Simplifying this equation, we get:
x^2 + 3025 = 2500
Subtracting 3025 from both sides, we have:
x^2 = 2500 - 3025
x^2 = -525
Since it's not possible to take the square root of a negative number, it seems like there might be an error in the given information or the problem setup.
Please double-check the given details and ensure they are accurate.
To solve this problem, we can use the Pythagorean theorem. Let's represent the distance from the boat to the anchor as 'x'.
According to the problem, the rope is 105 feet long, and the water is 55 feet deep. This forms a right triangle, where the hypotenuse is the length of the rope, the base is 'x', and the height is 55 feet.
Using the Pythagorean theorem, we have:
x^2 + 55^2 = 105^2
Simplifying this equation, we have:
x^2 + 3025 = 11025
x^2 = 11025 - 3025
x^2 = 8000
Taking the square root of both sides, we get:
x = √8000
x ≈ 89.4 feet
Therefore, the anchor is approximately 89.4 feet from the point directly below the boat.