Asked by Hot girl 2025😜
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
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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.
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.
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