# Angles A and C of triangle ABC are 67 and 83 degrees, respectively. Find BC if the radius

July 25, 2021 | education

| **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.