A ball with a radius R is inscribed in a cone whose generatrix is inclined to the base plane at an angle L. Find the height of the cone.
By the property of tangents drawn from one point, the segment OA divides the angle KAH in half, then the angle OAH = (L / 2) 0.
In the right-angled triangle AOH, we determine the length of the leg AH.
tgOAH = OH / AH = R / AH.
AH = R / tan (L / 2) = R * ctg (L / 2).
In a right-angled triangle ABH, we define the BH leg.
tgBAH = BH / AH.
BH = tgBAH * AH = tgL * R * ctg (L / 2).
Answer: The height of the cone is R * ctg (L / 2) * tgL.
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