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.