SOLUTION: Determine the vertical angle of a cone with height 20cm and radius 5cm

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Question 1179870: Determine the vertical angle of a cone with height 20cm and radius 5cm
Answer by MathLover1(20850) About Me  (Show Source):
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cone

Determine the vertical angle of a cone with
height h=20cm and
radius r=5cm
let the vertical angle be theta
use right triangle with sides the height h, radius r, and slant height l to find theta%2F2

using tan:

tan%28theta%2F2%29=5%2F20=1%2F4
theta%2F2=tan%5E-1%281%2F4%29
theta%2F2=14.04°
theta=2%2A14.04°
theta=28.08°


or, find slant height l and use cosine

l=sqrt%2820%5E2%2B5%5E2%29=20.615528
cos%28theta%2F2%29=h%2Fl=20%2F20.615528
theta%2F2=cos%5E-1%2820%2F20.615528%29
theta%2F2=14.04°
theta=28.08°

or use sine

sin%28theta%2F2%29=r%2Fl=5%2F20.615528128088304
sin%28theta%2F2%29=0.242535625

theta%2F2=sin%5E-1%280.242535625%29
theta%2F2=14.04°
theta=28.08°

so, the vertical angle of a cone with height 20cm and radius 5cm is 28.08°