Methods of finding line-plane angles

The methods of finding line-plane angles are the direct method, the three-cosine theorem, and the three-sine theorem.

1, direct method.

That is, the definition of the method, make the hypotenuse, the vertical line, the hypotenuse in the plane of the right triangle, according to the conditions of the hypotenuse and the hypotenuse of the angle that is required.

2, three cosine theorem.

Set the angle between the oblique and the plane is θ, in the plane to make a special line through the oblique foot, the line and the projectile angle θ, and it and the oblique angle γ or the rest of the chord, you can use the three cosine relationship cos γ = cos θ - cos β to find out the value of the cosine of the line surface angle.

3, three sine theorem.

Set the degree of dihedral angle M-AB-N is α, in the plane M there is a ray AC, which and the angle made by the prism AB is β, and the angle made by the plane N is γ, then sinγ=sinαsinβ.

Conclusion: the dihedral angle is the maximum of the line angle made by a straight line in the half-plane with the other half of the plane, i.e., the dihedral angle is the maximum value of the line angle.