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P is a point outside the plane where △ ABC is located. If △ ABC and △ PBC are regular triangles with side length 2, PA = 6, then the dihedral angle p-bc-a is______ °．
Take the midpoint D of BC to connect PD, ad, ∵ △ ABC, △ PBC are equilateral triangles, ∵ PD ⊥ BC, ad ⊥ BC, ∵ PDA is the plane angle of dihedral angle p-bc-a. PD = ad = 3, PA = 6, ∵ PDA = 90 degree. So the answer is 90 degree
Recently learning solid geometry, to the straight line and plane vertical I confused!
Especially, if we find two lines perpendicular to the same line, we can't find the intersection of the two lines. The theorem about this seems very abstract,
Find some three-dimensional graphics around, observe more, cultivate a sense of three-dimensional
There must be a straight line perpendicular to a diagonal line of the plane when solid geometry passes through a point in the plane?
There must be a straight line perpendicular to a diagonal line of the plane through which solid geometry passes
Is that right? Why?
Correct, as follows
Note that the intersection of the oblique line and the plane is a,
If the intersection plane of the perpendicular lines is point C, then AC is the projection of the oblique line,
Because the BC vertical plane,
So the plane is perpendicular to the plane ABC,
Because the line L passing through any point on the plane can be perpendicular to BC,
So line L is perpendicular to plane ABC, so line L is perpendicular to diagonal,
So there must be a straight line through a point in the plane perpendicular to a diagonal line of the plane
Sorry, there's no picture,
You can draw according to the above steps, it will be easier to understand
As shown in the figure, it is known that BC is the diameter of ⊙ o, P is the point on ⊙ o, a is the midpoint of BP, ad ⊥ BC is at point D, BP and ad intersect at point E, if ∠ ACB = 36 °, BC = 10. (1) find the length of AB; (2) prove: AE = be
(1) The length of ∵ AB is L = n π R180 = 72 × π × 5180 = 2 π. (2) it is proved that the ∵ point a is the midpoint of BP, the ∵ Ba = AP. ∵ C = ∵ ABP. ∵ BC is the diameter of ⊙ o, and the
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