The radii of the bases of the truncated cone are 3 and 6 cm, the generatrix – 5 cm. Find the cotangent of the angle
| July 2, 2021 | education
The radii of the bases of the truncated cone are 3 and 6 cm, the generatrix – 5 cm. Find the cotangent of the angle of inclination of the generatrix to the base plane.
The height BH divides the radius OA into segments AH and OH.
Since BО1ОН is a quadrangle, then ОН = BО1 = 3 cm.
Then AH = AO – OH = 6 – 3 = 3 cm.
In a right-angled triangle ABH, according to the Pythagorean theorem, we determine the length of the leg BH.
BH ^ 2 = AB ^ 2 – AH ^ 2 = 25 – 9 = 16.
BH = 4 cm.
The cotangent of the angle is the ratio of the length of the adjacent leg to the opposite one.
CtgА = АН / ВН = 3/4.
Answer: The cotangent of the angle is 3/4.
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