# showing that angle a/sin(a) in a circumscribed triangle is equal to the diameter of the circle

I am working my way through Saul and Gelfand's trigonometry.

An exercise within is as follows:

"Starting with an acute triangle, we can draw a circumscribed circle. If $\alpha$ is any one of the angles of the triangle, show that the ratio $\alpha$ :$sin$ $\alpha$ is equal to the diameter of the circle"

I know that we can get the diameter of a circle by multiplying the segment opposite an angle by the sin of the angle. I just don't understand how to obtain the measure of a line segment by using an angle.

• It says ".... ratio $a : \sin \alpha$", not $\alpha : \sin \alpha$ in here, and $a$ is presumably the opposite side of the triangle – user66081 Feb 5 '15 at 2:32
• Yeah that's what I thought. But how is ratio $\alpha$:sin $\alpha$ any different from $\alpha$:sin$\alpha$? – user183974 Feb 5 '15 at 2:42
• in the book it is "A : sin alpha", not "alpha : sin alpha" – user66081 Feb 5 '15 at 14:18