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Solve a high school mathematical geometry problem
1, certificate: According to the meaning of the question, there is BC⊥ surface AA 'c 'c.

∴A'C is the projection of A'B on aa' c' C surface.

Tan ∠ MAC = MC/AC = ∠ 2/2,Tan∠ACA′= A′A/AC =∠2。

∴tan∠mac*tan∠aca′= 1

∴∠mac+∠aca′=90

∴am⊥a′c

∴am⊥ba′

2. Certificate: According to the meaning of the question, there is BC⊥ face AA 'c 'c.

∴BC⊥AM

Conclusion in 1: AM⊥BA'

∴AM⊥ Noodles in BC

3. The meaning of this question is:

In the triangular pyramid M-ABC, MC⊥ plane ABC, ∠ ACB = 90, AC=√3, BC= 1, MC=√6/2.

The ∴ volume m-ABC V of a triangular pyramid = (BC * AC/2) * MC/3 = √ 2/4.

∴ Volume C-ABM V'=√2/4 of a triangular pyramid

According to the meaning of the question, AM=3√2/2, BM=√ 10/2, AB=2.

∴AB^2+BM^2=AM^2

The area of ∴△∴△abm is S=AB*BM/2=√ 10/2.

∴v′=s*h/3=(√ 10/6)h=√2/4

∴h=3√5/ 10

That is, the distance from point C to plane ABM is 3√5/ 10.

I will explain all this here. Of course, this is just my personal opinion. I hope it will help the landlord. . .