A cone is 8 cm high and it's vertical angle is 62 degrees. Find the diameter of it's base

Answer 1

h = height

r = radius

d = diameter

tan 62° = h / r

Multiply both sides by r

r ∙ tan 62° = h

Divide both sides by tan 62°

r = h / tan 62°

r = 8 / 1.88072646535

r = 4.25369 cm

d = 2 r = 2 ∙ 4.25369 cm = 8.50738 cm

d ≈ 8.5 cm

Answer 2

If by vertical angle you mean the angle formed by the point of the cone, then
r/8 = tan31°
d = 2r