If a boat leaves dock and travels 3 miles north, then travels 2.5 miles west, how many miles from the dock is the boat?
hint: Pythagoras
To find out how many miles from the dock the boat is, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the boat's path forms a right triangle, with the northward distance traveled being one side and the westward distance traveled being the other side.
So, we can calculate the total distance using the formula:
Distance = square root of (northward distance^2 + westward distance^2)
For this problem, the northward distance is 3 miles and the westward distance is 2.5 miles. Plugging these values into the formula, we have:
Distance = square root of (3^2 + 2.5^2)
Distance = square root of (9 + 6.25)
Distance = square root of 15.25
Distance ≈ 3.91 miles
Therefore, the boat is approximately 3.91 miles from the dock.