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

bystudin | 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

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.