How to find dihedral angle?

How to find the dihedral angle? Please explain all the methods in detail.

Common methods:

The first method is the definition method, just follow the definition, which is not common.

the second method is the angle finding method of the three perpendicular theorem, which is also the most common. For example: to find dihedral angle A-CD-B, then A is the vertical line of BCD plane, and E is the vertical line of CD, and F is the vertical line of CD, connecting FA, and then the angle AFE is the plane angle of dihedral angle.

the third clock is area photography. If the area of triangle ABC in face 1 is S1, and the area of projection triangle DEF of ABC in face 1 is S2, then the cosine of dihedral angle of 1,2 is S2/S1.

Finally, after knowing the method, you should do more exercises to accumulate experience in order to make a concrete analysis of specific topics, so that you can be handy when doing exercises.

How to determine dihedral angles?

the angle formed by two half planes is the dihedral angle.

generally, take a point a from one surface, cross it to make it perpendicular to the other surface, cross it to b, cross b to make it perpendicular to the intersection of the two surfaces, and cross it to c, then the angle ACB is the plane angle of the dihedral angle.

method of finding dihedral angle (the more detailed the better)

The most important thing in finding dihedral angle is to find the plane angle of dihedral angle

The most important point of this dihedral angle is that both sides of the angle must be perpendicular to the intersection line of two faces

There are two common methods to find the plane of dihedral angle:

Plane α and Plane β, intersection line L, and a point in space P < But not on the intersection line L

make the vertical line of plane β, the vertical foot is H, and the vertical foot is A, connecting AP, and the angle PAH is the plane angle of dihedral angle

2)P on the intersection line L

make rays PA and PB perpendicular to L in planes α and β respectively, and the angle APB is the plane angle of dihedral angle < p. The vertical foot is a, and the angle BAH is the plane angle of dihedral angle < P > In a word, the key is that both sides of the angle must be perpendicular to the intersection of two biting surfaces, and it should be noted that dihedral angle can be obtuse, depending on the specific situation.

If I tell you exactly what A-l-B looks like, even if the angle is

, there may be two solutions when I only ask you about the plane and the plane

How to find the dihedral angle?

find the intersection of dihedral angles. . . . Then find two sides perpendicular to this intersection line, one side falls in one of the faces and the other side falls in the other face.

and these two sides intersect at a point. . . That is to say, the intersection line is perpendicular to a plane formed by the straight lines of these two sides.

at this time, the angle formed by these two sides is the dihedral angle. . .

how to find the plane angle of dihedral angle

1. Make the perpendicular of the intersection line of two planes in two planes through the same point, and the included angle of these two intersection lines is the plane angle corresponding to dihedral angle

2. You can make a vertical plane through a point on the edge, and the angle formed by the intersection line with two planes is the plane angle

How to find the dihedral angle in geometry

Suppose that plane α and.

are you studying compulsory 2 now? In fact, when you do solid geometry in the college entrance examination, you basically don't need the knowledge of compulsory 2. In compulsory 4, you have to learn plane vectors, and you have to learn space vectors in the elective course. In the future, you will rely on vectors to algebra solid geometry problems for calculation. < P > How to find the plane angle of dihedral angle? How to find the dihedral angle when two planes intersect at a point to find the great god

to be vertical

? Don't look at the picture

If a point on the intersection line of two planes is perpendicular to the intersection line in the two planes, the included angle between the two perpendicular lines is the dihedral angle of the two planes.