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

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.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.