This is a short video deriving the Law of Sines. GIven any triangle ABC, the following relation holds:
a / sin A = b / sin B = c / sin C = 2r ( where r is the radius of the triangle's circumcircle )
Music: "Devote for Nature" by Noriyuki Iwadare ( Radiata Stories OST - Playstation 2 )
The main reason why the circumcircle was constructed was to derive the
Law of Sines from the properties of inscribed angles in the circle, together
with the definition of the trigonometric functions in a right triangle.
It is easy to know the area and circumference of the circumcircle if information
about the triangle is given. All you need is to solve for "R" according to the
formula shown in the video and then use A = pi * R^2, C = 2 * pi * R
maths486 1 year ago