The height of the cone is equal to the radius of the base. What is the angle between the generatrix and the base of the cone?
| September 7, 2021 | education
Let’s draw an axial section of the cone, which is an isosceles triangle ABC, AC = BC as generators of the cone.
The height of the OC of the cone is the bisector, the height and median of the triangle ABC, then the triangles AOC and BOC are rectangular. Since, by condition, the height of the cone is equal to the radius of the circle at its base, then AO = OC, and the right-angled triangle AOC is isosceles.
Angle ОАC = ОCА = (180 – 90) / 2 = 45.
Answer: The angle between the generatrix and the base of the cone is 45.
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