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. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the depth of the water represents one side of the right triangle, and the distance between the anchor and the point directly below the boat represents the other side. The length of the rope connecting the boat to the anchor acts as the hypotenuse.
Let's represent the distance between the anchor and the point directly below the boat as 'x'. Applying the Pythagorean theorem, we can set up the following equation:
x² + 55² = 105²
Now, let's solve for 'x':
x² + 3025 = 11025
x² = 11025 - 3025
x² = 8000
x ≈ √8000
x ≈ 89.4 feet
Therefore, the anchor is approximately 89.4 feet away from the point directly below the boat.
Another Pythagoras question
x^2 + 55^2 = 105^2
x^2 = 105^2 - 55^2
x = √(105^2 - 55^2)
= ......