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Please help precalculus

Please help precalculus-example-1

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We have Law of Cosines for a and then for the two angles, really only one angle because they'll add to 180 degrees.

b=9, c=11, A=56°

a² = b² + c² - 2bc cos A

a² = 9² + 11² - 2(9)(11) cos(56) ≈ 91.2798

a ≈ 9.554

b² = a² + c² - 2ac cos B

2ac cos B = a² +c² - b²

cos B = (a² +c² - b²) / 2ac

cos B ≈ (91.2798 + 11² - 9²) / 2(9.554)(11) ≈ 0.62458

B ≈ arccos 0.62458 ≈51.348 degrees

Looking at the choices we don't need to bother with C,

Answer: A a=9.6, B=51.4 deg

User Roman Liutikov
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