Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
An obtuse triangle with sides 119 miles, 94 miles, and 173 miles. The side labeled 173 is a dotted line segment. Dotted line at the bottom left extends to the left with an angle x.
Use the Law of Cosines to solve the problem.
A ship travels due west for 94 miles. It then travels in 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 direction? Show your work.
To find the angle x, we can use the Law of Cosines:
c^2 = a^2 + b^2 - 2ab * cos(C)
Where c is the side opposite the angle we are trying to find (173 miles), and a and b are the other two sides (94 miles and 119 miles).
Plugging in the values:
173^2 = 94^2 + 119^2 - 2*94*119 * cos(x)
29929 = 8836 + 14161 - 22412 * cos(x)
29929 = 22997 - 22412 * cos(x)
6946 = -22412 * cos(x)
cos(x) = -6946 / 22412
cos(x) = -0.3097
x = cos^(-1) (-0.3097)
x ≈ 108.9 degrees
Therefore, the ship turned approximately 108.9 degrees north of west when it changed direction.