7
QuizMultiple Choice

Law of Cosines — Quiz

Question 7 • Precalculus

A ship heads due north for x miles, then turns 25 degrees east of north and travels for another y miles. Which expression represents the distance the ship is from the original starting point?

Answer
A
x plus y minus square root of 2 x y cosine 155 degrees end root
B
square root of x squared plus y squared minus 2 x y cosine 25 degrees end root
C
square root of x squared plus y squared minus 2 x y cosine 155 degrees end root
D
x plus y minus square root of 2 x y cosine 25 degrees end root

Explanation

The ship’s two displacement vectors have lengths x and y, with an angle of 25° between them. In the triangle from the start to the endpoint, the included angle is 155° because the first leg points south when viewed from the endpoint. By the law of cosines, the distance is √(x² + y² − 2xy cos 155°), which is choice C.

AI-written and checked against the verified answer.

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