Question

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

Answer 1

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.