Sine law or cosine law? Word problems

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Learn it Choose the law from what you know. A side and its opposite angle (plus one more) → sine law. Two sides and the angle between them, or all three sides → cosine law.

Example: Two boats leave a dock at an angle of 70°, one going 12 km and the other 15 km. How far apart are they?

Two sides and the angle between them: cosine law.
d² = 144 + 225 − 2(12)(15) cos 70° ≈ 245.9.
d ≈ 15.7 km.

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