A sector of 144 degrees is removed from a circle of radius 15, and the remaining portion is folded into a cone. What is the angle at the vertex of the cone?
The cone will now hav a circumference of pi * 30 - pi*30 (144/360) = 56.549 units
this will be a diameter of 56.549/pi = 18 radius of 9 units
the side length will still be 15 units
sin of 1/2 of the vertex = opp / hyp = 9/15
arcsin (9/15 ) = 36.87 degrees 2 x 36.87 = 73.74 degrees