Angles A and C of triangle ABC are 67 and 83 degrees, respectively. Find BC if the radius of the circle around triangle ABC is 16.
The sum of the inner angles of the triangle is 180, then the angle BAC = (180 – ABC – ACB) = (180 – 67 – 83) = 30.
Use the sine tower for the triangle.
2 * R = BC / SinA = AC / SinB = AB / SinC.
2 * R = BC / SinA.
BC = 2 * R * Sin30 = 2 * 16 * (1/2) = 16 cm.
Answer: The length of the BC side is 16 cm.
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