In a triangle ABC, the AC side is a, the angle A = alpha, the angle B = beta. Find the area of the triangle.
| February 12, 2021 | education
Using the sine theorem, we define the length of the BC side.
BC / Sinα = AC / Sinβ.
ВС = AC * Sinα / Sinβ = a * Sinα / Sinβ.
Angle АСВ = (180 – (α + β)).
Then, the area of the triangle ABC will be equal to:
Sас = АС * ВС * SinACB / 2 = a * (a * Sinα / Sinβ) * Sin (180 – (α + β)) / 2 = a2 * Sinα * Sin (α + β) / 2 * Sinβ.
Answer: The area of a triangle is a2 * Sinα * Sin (α + β) / 2 * Sinβ.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
