In triangle ABC AB: BC = 2: 3, BH-height, angle C = 30 degrees. Find AB + BC if BH = 6cm.

univerkov | December 6, 2020 | education

Angle C = 30 °, BHC = 90 °, then BHC is a right triangle. The angle opposite 30 ° is equal to half of the hypotenuse, so if AB = 2x, BC = 3x, then BH = 1.5x. By the condition BH = 6, then X = 6: 1.5 = 4. Then AB = 8, BC = 12, then AB + BC = 20.
Answer: 20

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