若CD为Rt△ABC的斜边AB上的高,显然有sin~2A+sin~2B=sin~2∠CDA。若γf△ABC所在的平面β与AB所在平面α垂直,则角A、B分别是直角边CA,CB与α所成的角,而∠CDA与二面角β-AB-α的平面角相等,于是有:两直角边与α所成角的正弦的平方和等于α与β所成角的正弦的平方。有意思的是,α与β不垂直时,上述结论仍立。即有命题: 若Rt△ABC所在的平面β与斜边AB所在的平面α成角θ,则两直角边与α所成角的正 If CD is high on the hypotenuse AB of Rt △ ABC, there is obviously sin~2A+sin~2B=sin~2∠CDA. If γfΔABC lies in the plane β and the plane α of the AB is perpendicular, the angles A and B are the angles of the right-angled edge CA, CB and α, respectively, and the planar angles of the ∠CDA and the dihedral angle β-AB-α are equal. Therefore, the square sum of the sine of the angle formed by two right-angled edges and α is equal to the square of the sine of the angle formed by α and β. Interestingly, the above conclusion is still valid when α and β are not perpendicular. That is, if there is a proposition: If the plane β where RtΔABC is located and the plane α where the hypotenuse AB is located forms an angle θ, then the angle formed by the two right-angle edges and α