Final answer:
The ship has traveled 10.2 nautical miles due north, calculated using the Pythagorean theorem based on the overall distance from the starting point and the eastward travel.
Step-by-step explanation:
To find the distance the ship traveled due north, we can apply the Pythagorean theorem to the right-angled triangle formed by the eastward and northward travels of the ship. The total distance from the starting point to the final position (hypotenuse) is given as 15.2 nautical miles, and the eastward distance (one of the legs) is 11.3 nautical miles.
We can calculate the distance traveled north (the other leg) using the formula:
c2 = a2 + b2, where c is the hypotenuse, and a and b
are the legs of the right triangle.
By rearranging the formula to solve for
b
, we get:
b = √(c2 - a2
Substituting the given values:
b = √(15.22 - 11.32
Therefore, the ship traveled 10.2 nautical miles due north.