In a regular hexagonal prism ABCDEFA1B1C1D1E1F1 all edges are equal to 31. Find the tangent of the angle AD1D.
| May 7, 2021 | education
Since a regular hexagon lies at the base of the prism, the radius of the circle described around it is equal to the length of the side of the regular hexagon, R = AB = 31 cm.
The large diagonals of the hexagon are equal to the diameter of the circumscribed circle, then AD = D = 2 * R = 2 * 31 = 62 cm.
Triangle ADD1 is rectangular with a right angle at point D, then tgAD1D = AD / DD1 = 62/31 = 2.
Answer: The tangent of the ADD1 angle is 2.
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