A ship has steamed 120 nautical miles North and 230 nautical miles West.
The ship has traveled a total distance of 120 + 230 = <<120+230=350>>350 nautical miles.
To determine the total displacement of the ship, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse (the longest side of a right triangle) is equal to the sum of the squares of the other two sides.
In this case, the ship has steamed 120 nautical miles North and 230 nautical miles West, which forms a right triangle where the North leg is the height and the West leg is the base.
Let's proceed with the calculation:
Step 1: Square the length of the North leg.
120^2 = 14,400.
Step 2: Square the length of the West leg.
230^2 = 52,900.
Step 3: Add the squared lengths of the North and West legs.
14,400 + 52,900 = 67,300.
Step 4: Take the square root of the sum calculated in step 3 to find the length of the hypotenuse.
√67,300 ≈ 259.45.
Therefore, the ship's total displacement, or the length of the hypotenuse, is approximately 259.45 nautical miles.