A ship travels due west for 83 miles. It then travels in a northwest direction for 111 miles and ends up 165 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.

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A ship travels due west for 83 miles. It then travels in a northwest direction for 111 miles and ends up 165 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.

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it turned 115.8 °

Step by step explanation:

The triangle created is shown in the attached photo. The angle at which the ship turns in a northwesterly direction is ange A. To determine angle A, we would apply Cosines’ law expressed as

a² = b² + c² – 2abCosA

Where a, b and c are the lengths of each side of the triangle and A is the angle corresponding to a. Like the expression with the given triangle, it rises

165² = 111² + 83² – 2 (111 × 83) CosA

27225 = 12321 + 6889 – 2 (9213) CosA

27225 = 19210 – 18426CosA

18426CosA = 19210 – 27225

18426CosA = – 8015

CosA = – 8015/18426

CosA = – 0.435

A = Cos ^ – 1 (- 0.435)

A = 115.8 ° to the nearest tenth