Finding dihedral angle (or sine or cosine) is a common problem in solid geometry. There are usually three ways to solve this kind of problem:

(1) is calculated directly from the plane angle of dihedral angle;

(2) projection method: calculate the dihedral cosine according to the projection area;

(3) Vector method: calculate according to the normal vectors of two surfaces;

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Note: it is an isosceles right triangle, not a regular triangle;

As the midpoint, it is the plane angle of dihedral angle;

Using cosine theorem, the cosine value of this angle can be easily obtained.

Reference answer: 20 17 national volume a 18

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This problem is more difficult and can be solved by plane angle.

Reference answer: 20 18 Mathematics and Mathematics National Volume C 19

Reference answer: 2065438+2008 national volume mathematics and mathematics problem B 20

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This problem can be solved by vector method or geometric method.

Geometric methods are needed as auxiliary lines: the intersection of connection and record is; Take the midpoint and make.

The geometric model of this question appears many times in the college entrance examination, so we must be familiar with its characteristics: it is a regular triangle and an isosceles right triangle;

It is three congruent right-angled triangles.

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This problem can be solved by projection method or plane angle method.

Note that this pattern appears many times in the college entrance examination.

Reference answer: 2004 national liberal arts mathematics volume 2 1

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Reference answer: 2007 Mathematics Hainan Volume 18.

Tip: The cosine of dihedral angle can be calculated by the area ratio of two triangles. For reference, please refer to the following questions: 2004 national literature volume, three questions, 2 1.

Reference answer: 20 12 math problem 19

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This problem can be solved by vector method or projection method.

In contrast, the projection method is concise and elegant, and the amount of calculation is small.

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This big topic of 20 19 is similar to that of 20 12; It can be solved by projection method; Of course, it can also be solved by vector method.

Reference answer: 20 19 national mathematics, question a, 18.

Cracking strategy

This problem can be solved by projection.

The dihedral angle can be divided into two parts:.

It is a straight dihedral angle, so just find the sine value of.

Is the projection, calculate the area ratio of these two triangles, and the problem will be solved.

Reference answer: 20 1 1 National Mathematics Examination 18.

Cracking strategy

For this problem, most teaching AIDS only provide vector solution; In fact, this problem can also be solved by projection.

Usually, if you do more training with more than one question, you will have more initiative in the examination room.

See: 20 17, Question C of Mathematical Mathematics in the National Volume 19.

Cracking strategy

This problem can be solved by both vector method and plane angle method.

The key to using vector method is that it is perpendicular to each other, which can be used to establish rectangular coordinate system.

The key to solving by geometric method lies in: the edge of dihedral angle of the solution is required;

Plane and vertical.

Vector solution: National Volume A Question 2020 18

Geometric Solution: Question A of National Volume 2020 18

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Reference answer: 20 18 mathematics national volume a 18: solving with pythagorean theorem

Reference answer: 20 18 mathematics national volume a 18: solve with volume formula.

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This is a test question to test the spatial imagination.

In fact, it is possible to solve it by vector method or plane angle method.

Reference answer: 20 19 Mathematics and Mathematics National Volume C 19

Reference answer: 2020 National Volume B Question 20

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Reference answer: 20 14 math volume a 19

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Reference answer: Question C of National Volume 2020 19

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Reference answer: 20 17 national science mathematics volume b 19

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Reference answer: 20 16 national mathematics volume a 18

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Reference answer: 20 13 national volume mathematics and mathematics question b 18

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