A = 55 degrees. B = 65 degrees. AB = 18√3, find the diameter of the circle circumscribed about the triangle ABC.

univerkov | September 6, 2021 | education

The radius of the circumscribed circle around a triangle is equal to the ratio of the length of the side of the triangle to two values of the sine of the angle opposite to this side.

R = AB / 2 * SinBCA.

Determine the value of the angle of the BCA.

BCA angle = 180 – ABC – BAC = 180 – 65 – 55 = 60.

Then: R = (18 * √3) / 2 * Sin60 = 9 * √3 / (√3 / 2) = 18 cm.

Then the diameter of the circle is: D = 2 * R = 2 * 18 = 36 cm.

Answer: The diameter of the circle is 36 cm.

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