3.a ship travels due west for 60 miles. it then travels in a northwest direction for 85 miles and ends up 119 miles from its original position. to the nearest tenth of a degree, how many degrees north of west did it turn when it changed direction? show your work.

Given:

due west: 60 miles

northwest: 85 miles

original point to destination point: 119 miles

Let us use the Law of Cosines to find the angle.

119² = 60² + 85² - [(2*60*85)*cos(x)]

14,161 = 3600 + 7225 - (10,200 * cos(x))

14,161 = 10,825 - 10,200 cos(x)

14,161 - 10,825 = -10,200 cos(x)

3.336 = -10,200 cos(x)
3,336 / -10,200 = cos(x)

-0.3271 = cos(x)

-0.3271 / cos = x

cos^-1 (-0.3271) = x

109.09 = x

109.09° or 109.10° north of west.

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