# A ball with a radius R is inscribed in a cone whose generatrix is inclined to the base plane at an angle L.

June 30, 2021 | education

| **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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