The angle of a triangle is 2: 3: 7, and its smallest side is a. Find the radius of the circle circumscribed about it.

univerkov | October 8, 2021 | education

Let the angle BAC = 2 * X, angle ACB = 3 * X, angle ABC = 7 * X.

Then 2 * X + 3 * X + 7 * X = 180.

12 * X = 180.

X = 180/12 = 15.

Then the smallest angle BAC = 2 * 15 = 300.

Then the radius of the circumscribed circle is:

R = BC / 2 * Sin30 = a / 2 * (1/2) = a cm.

Answer: The radius of the circumscribed circle is a cm.

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