Angles B and C of triangle ABC are 65 ° and 85 °, respectively. Find BC if the radius of the circle

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

Let us find the angle A. By the theorem on the sum of the angles of a triangle, it is known that the sum of all interior angles of any triangle is equal to 180 degrees. Then:
angle A + angle B + angle C = 180 radices;
angle A + 65 degrees + 85 degrees = 180 degrees;
angle A = 180 degrees – 150 degrees;
angle A = 30 degrees.
By the theorem of sines, it is known that the sides of a triangle are proportional to the sines of the opposite angles:
AC / sinB = AB / sin C = BC / sin A = R,
where AC, AB and BC are the sides of the triangle ABC, sinB, sin C and sin A are the sines of the angles opposite to the sides of AC, AB and BC, respectively.
BC / sin A = R;
BC = sin30 * 14;
BC = ½ * 14 = 14/2 = 7 (conventional units).
Answer: BC = 7 conventional units.