Find the generatrix of the cone, the height of which is 12 cm, and the generatrix is inclined to the base
April 2, 2021 | education
| Find the generatrix of the cone, the height of which is 12 cm, and the generatrix is inclined to the base plane at an angle of 45 °.
Consider a right-angled triangle formed by the height of the cone, the radius of its base and the generatrix. Height – leg, opposite to the angle between the generatrix and the base plane, the generatrix – hypotenuse. The ratio of the opposite leg to the hypotenuse is the sine of the angle. Means:
sin 45 ° = h / L.
Hence:
L = h / sin 45 ° = 12 / (√2 / 2) = 12√2 ≈ 16.97 cm.
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