# In the triangle KMN, the angle is K = 80 degrees. angle = 40 degrees. KN = 6cm. Find the radius of the circle around the triangle.

January 19, 2021 | education

| Determine the value of the angle KMN of the triangle.

Angle KMN = 180 – MKN – MNK = 180 – 80 – 40 = 60.

The diameter of the circumscribed circle around a triangle is equal to the ratio of the length of the side of the triangle to the sine of the opposite angle. Then the radius will be equal to:

ОМ = R = (KN / 2 * SINkmn) = 6/2 * Sin600 = 3 / (√3 / 2) = 6 / √3 = 2 * √3 cm.

Answer: The radius of the circumscribed circle is 2 * √3 cm.

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