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FrozenT [24]
3 years ago
6

Please help! 30 points!

Mathematics
1 answer:
Rashid [163]3 years ago
8 0

Answer: 64.2^{\circ}

Step-by-step explanation:

According to the cosine rule

\cos C=\dfrac{a^2+b^2-c^2}{2ab}

Here, a=83, b=111, c=165,\ C=180^{\circ}-\theta

Putting values

\Rightarrow \cos (180^{\circ}-\theta)=\dfrac{83^2+111^2-165^2}{2\times 83\times 111}\\\\\Rightarrow \cos(180^{\circ}-\theta)=\dfrac{6889+12321-27225}{18426}\\\\\Rightarrow \cos(180^{\circ}-\theta)=\dfrac{-8015}{18426}=-0.4349\\\\\Rightarrow 180^{\circ}-\theta=\cos^{-1}(-0.4349)=115.77^{\circ}\\\Rightarrow \theta=64.23\approx 64.2^{\circ}

So, the ship turns by 64.2^{\circ} north of west

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