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Senior one mathematics space geometry proof problem
Take point E in BC to connect A 1E with AE, and it, AB and AC are all 60 degrees. The straight line AE is the projection of the oblique line AA 1 on the AB and AC planes, and then we can get that it is the root number of three molecules, the length of AA 1 is the root number of two molecules 3a, and the cosine value of the visible angle AA 1E is equal to the AE ratio AA65438.

For example, the second question is the height of the four cones A-CBB 1C 1. The volume of the four cones A-CBB 1C 1 can be obtained by volume subtraction, which is naturally obtained.

Thirdly, when calculating the volume, the height of pituitary gland is A 1E, which is very convenient to calculate. It is also necessary to prove that the heights of parallelogram ACC 1A 1 and parallelogram ABB 1A 1 are higher than the sine value of AA 1 multiplied by 60 degrees.