# The angles B and C of triangle ABC are 65 ° and 85 °, respectively. Find BC if the radius of the circle circumscribed around triangle ABC is 14

May 31, 2020 | Education

| By the theorem on the sum of the angles of a triangle:

180 ° = ∠A + ∠B + ∠C

180 ° = ∠A + 65 ° + 85 °

∠A = 180 ° -65 ° -85 ° = 30 °

By the sine theorem:

2R = BC / sin∠A

2R = BC / sin30 ° = BC / (1/2) = 2BC

R = BC = 14

Answer: 14

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