# In triangle ABC, angle A = alpha, angle B = beta, BC = a. Find the area of the triangle and the radius of the circle around it.

May 30, 2021 | education

| We use the sine theorem to determine the length of the AS.

AC / Sinα = BC / Sinβ.

AC = BC * Sinα / Sinβ = a * Sinα / Sinβ see

Let’s determine the value of the angle ACB.

Angle ACB = (180 – (α + β)).

Let’s calculate the area of the triangle ABC.

Sас = АС * ВС * SinACB / 2 = (a * Sinα / Sinβ) * a * Sin (α + β) / 2 = a ^ 2 * Sinα * Sin (α + β) / 2 * Sinβ cm2.

The radius of the circumscribed circle will be equal to:

R = BC / 2 * SinBAC = a / 2 * Sinα see.

Answer: The area of the triangle is a ^ 2 * Sinα * Sin (α + β) / 2 * Sinβ cm2, the radius of the circumscribed circle is a / 2 * Sinα cm.

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