In triangle ABC AC = 10, angle BAC = 70 degrees, angle ACB = 80 degrees. Find the radius of the circle
| August 30, 2021 | education
In triangle ABC AC = 10, angle BAC = 70 degrees, angle ACB = 80 degrees. Find the radius of the circle around this triangle
In solving the problem, we will use the theorem of sines. To do this, we find the angle ABC, located opposite the side of the AC.
∠ ABC = 180 ° – (∠ BAC + ∠ ACB) = 180 ° – 150 ° = 30 °.
By the sine theorem, we write the equality:
2R = AC / sin 30 ° = 10 / 1/2 = 20.
R = 10.
Answer: the radius of the circumscribed circle is 10.
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.
