# 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.

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