As shown in the figure, it is known that all edges of the regular triangular prism abc-a1b1c1 are equal in length, and D is the midpoint of a1c1, then the sine value of the angle between the straight line AD and the plane b1dc is______ ．

As shown in the figure, it is easy to prove b1d ⊥ plane AC1 by connecting b1d, and make Ag ⊥ CD through point a, then Ag ⊥ b1d can be obtained from b1d ⊥ plane AC1, and Ag ⊥ plane b1dc can be obtained from the judgment theorem of perpendicularity of line and plane, then ⊥ ADG is the angle between straight line AD and plane b1dc. If the edge length is known, it is possible to make it 2, then ad = 5 = CD, and Ag = AC × AA & nbsp; can be obtained from the equal area method; 1CD = 455, so the sine value of line AD and plane DCB1 is 45, so the answer is 45

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1. In the regular triangular prism abc-a1b1c1, if all edges are equal in length, then the tangent of the angle between the straight line CB1 and the plane aa1b1b is () A. Root 15 / 3 B. root 15 / 5 C. root 5 / 5 d. root 2
2. It is known that the lengths of the side edges and the bottom edges of the triangular prism abc-a1b1c1 are equal, and the projection of A1 on the bottom ABC is the midpoint D of the BC edge, then the cosine value of the angle formed by the out of plane line AB and CC1 is: A、(√3)/4 B、(√5)/4 C、(√7)/4 D、3/4 Please give me a picture of this problem. There are a lot of pictures in the process of solution
3. It is known that the side edge and the bottom edge of the triangular prism abc-a1b1c1 are equal, and the projection of A1 in the ground ABC is the center of ABC, What is the cosine of AB and CC1
4. It is known that the side edges and the bottom sides of the triangular prism abc-a1b1c1 are equal, and the projection D of A1 on the bottom ABC is the midpoint of BC, then the cosine value of the angle between AB and CC1 is? Trouble with space vector and solid geometry method to give solutions
5. It is known that the side edges of the triangular prism abc-a1b1c1 are equal to the sides of the bottom. The projection of A1 in the plane ABC is △ ABC It is known that the side edges and the bottom sides of the triangular prism abc-a1b1c1 are equal, and the projection of A1 in plane ABC is the center of △ ABC, then the sine value of the angle between Ab1 and plane ABC is △ ABC To process! Write a good reward to
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