A ship travels due West for 94 miles it then travels into a Northwest direction for 119 miles and ends up 173 miles from its original position to the nearest tenth of a degree how many degrees north of West (x) did it turn when it changed directions
We can solve this problem using the Law of Cosines. Let's call the angle between the ship's initial direction and its final direction "x". Then, we can use the following formula:
c^2 = a^2 + b^2 - 2ab*cos(x)
where c is the distance between the ship's starting and ending positions (173 miles), a is the distance traveled due West (94 miles), b is the distance traveled in a Northwest direction (119 miles), and x is the angle we're trying to find.
Plugging in the values we know, we get:
173^2 = 94^2 + 119^2 - 2(94)(119)*cos(x)
Simplifying this equation, we get:
29929 = 11236 - 22486*cos(x)
Rearranging and dividing by -22486, we get:
cos(x) = (11236 - 29929)/22486 = -0.928
Taking the inverse cosine of both sides, we get:
x = 126.5 degrees
Therefore, the ship turned approximately 126.5 degrees north of West when it changed directions.