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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1. In the triangle ABC, ∠ a = 80 degrees, the bisector of the outer angles of ∠ B and ∠ C intersects point O, and ∠ BOC?
2. In the triangle ABC, where ∠ a = 40 ° and O is the intersection of the bisectors of ∠ ABC and ∠ ACB, then ∠ BOC=______ ．
3. It is known that in △ ABC, ∠ a = 60 ° and the bisectors of ∠ ABC and ∠ ACB intersect at point O, then the degree of ∠ BOC is 0______ Degree
4. It is known that, as shown in the figure, in △ ABC, the bisector of ∠ ABC and ∠ ACB intersects at point o
5. In the straight triangular prism abc-a1b1c1, if ∠ BAC = 90 ° AB = AC = Aa1, then the angle between the out of plane straight line BA1 and AC1 is equal to () A. 30°B. 45°C. 60°D. 90°
6. As shown in the figure, BD and CE are the heights of △ ABC, and BD = CE
7. In the straight triangular prism abc-a1b1c1, Aa1 = BC = AB = 2, AB is perpendicular to BC, find the size of dihedral angle b1-a1c-c1, which two planes are b1-a1c-c1? Just type a word. I already know it, No one wants points
8. Prove three high intersection of triangle and one point
9. Ask a math problem about vectors and triangles? O is always a point in the triangle ABC, and there are: OA ^ 2 + BC ^ 2 = ob ^ 2 + Ca ^ 2 = OC ^ 2 + AB ^ 2, proving: ab ⊥ OC. Note: in the condition, OA, BC, ob, CA, OC, AB are the form of module length of vector; in proving, AB and OC are the form of vector
10. Mathematical problems about vectors In △ ABC, satisfy: ab ⊥ AC, M is the midpoint of BC (1) If | ab | = | AC |, find the cosine of the angle between vector AB + 2Ac and vector 2Ab + AC; (2) If O is any point on the line am, and | ab | = | AC |, = root 2, find the minimum value of OA * ob + OC * OA (3) If P is a point on BC, and AP = 2, AP * AC = 2AP * AB = 2, find the minimum value of | AB + AC + AP |
11. 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
12. 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
13. 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
14. 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
15. 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______ ．
16. It is known that each edge length of oblique triangular prism abc-a1b1c1 is 1, and the angle a1ab = angle a1ac = 60 degrees How to prove bcc1b1 as a square
17. In the regular triangular prism abc-a1b1c1, if AB = 2 and a & nbsp; A1 = 1, then the distance from point a to plane a1bc is () A. 34B. 32C. 334D. 3
18. In the straight triangular prism abc-a1b1c1, ∠ ACB = 90 ° Aa1 = AC = a, then the distance from point a to plane a1bc is?
19. In the triangular prism abc-a1b1c1, ab = AC = 2aa1, ∠ baa1 = ∠ caa1 = 60 °, D and E are the midpoint of AB and A1C respectively
20. In the regular triangular prism abc-a1b1c1, ab = 2, Aa1 = 1, find the distance from point a to plane a1bc