Start by conceptualizing the journey of the ship into a right-angle triangle. The initial journey due north forms one side of the triangle and is given as 320 miles. The eastward journey after turning forms the other side and is given as 200 miles.
The ship’s distance from the starting point at the end of its eastward journey will be the diagonal or the hypotenuse of this right triangle. So, we need to calculate the length of the hypotenuse of a right triangle with sides 320 miles and 200 miles long.
We can use the Pythagorean theorem to determine the solution to this problem. The Pythagorean theorem is represented mathematically as a^2 + b^2 = c^2, where a and b are the lengths of the sides of the right-angle triangle, and c is the length of the hypotenuse.
To find the desired distance (or hypotenuse), we substitute the given distances into the Pythagorean theorem. Let 320 miles be represented by a, and 200 miles be represented by b. Then:
a^2 + b^2 = c^2
(320 miles)^2 + (200 miles)^2 = c^2
102400 miles + 40000 miles = c^2
142400 miles = c^2
Square root of 142400 miles = c
c = -+377.35924528226417 miles.
Considering distance cannot be negative and the value is rounded to the nearest mile, the ship from its starting point is approximately 377 miles.