A 160 degree of a sector radius 10.5cm is bent to form a cone,find the vertical angle of the cone

Answer 1

make a sketch to see that the 10.5 cm becomes the hypotenuse of the cone and the circumference of the cone is the arc length of the sector.
160° = 160/180π radians
= 2.7925.. radians
arc = 2.7925(10.5) = 29.32153..

this becomes the circumf of the base of the cone
2πr = 2932153
r = 4.666... = 4 2/3 = 14/3

If 2Ø is the vertical angle, then
sinØ = 4.6666.../10.5
Ø = 26.387..
2Ø = 52.78°

Answer 2

We all that sine is equal to opposite over hypotenuse.If you sketch your diagram.The opposite will be 10.5cm while the 160°will be your hypotenuse. Area of a sector of a circle=160/360=0.444. Sine theta=160/360.sine theta=0.444. inverse of sine gives you 26.356. Vertical angle=2*theta will give 2*26.356=52.718.Then your vertical angle will be 53°(to the nearest degree).