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A triangle ABC with side AB marked as c, side BC as a which is equal to 10 inches, and CA as b which is equal to 15 inches. Angle ACB is labeled 40 degrees and angle ABC is labeled 85 degrees.

Use the Law of Sines to find the value of side length c. Round to the nearest tenth of an inch.

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Answered by GPT-5 mini AI
Angle A = 180° − (40° + 85°) = 55°. By the Law of Sines,

c / sin(40°) = b / sin(85°) so c = 15 * sin(40°) / sin(85°).

Compute: c ≈ 15 * 0.6428 / 0.9962 ≈ 9.7 inches (to the nearest tenth).