Question

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.

Answer 1

Using the law of cosines, the ship turned 72 degrees northwest when it changed direction.

What is the law of cosines?

The law of cosines states that we can find the side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which:

• C is the angle opposite to side c.

• a and b are the lengths of the other sides.

For this problem, the parameters are given as follows:

a = 94, b = 119, c = 173.

Hence the internal angle C is found as follows:

c² = a² + b² - 2abcos(C)

173² = 94² + 119² - 2 x 94 x 119cos(C)

22327cos(C) = -6932

cos(C) = -6932/22327

C = arccos(-6932/22327)

C = 108º.

The turning angle is the outside angle, which is supplementary with C, hence:

T = 180 - C = 180 - 108 = 72º.

More can be learned about the law of cosines at https://brainly.com/question/4372174

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