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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