求二面角的大小是立几中的重点和难点 ,但有时苦于难作二面角的平面角 ,或平面角虽作出 ,但计算繁琐 .可以发现 ,利用下面的公式 ,常能摆脱上述的困境 .定理　如图 1 ,四面体 P - ABC中 ,PC⊥面 ABC,∠ PAC =α,∠ BAC =β,二面角P - AB - C的大小为θ,则tanθ =tanαsinβ.证? The size of the dihedral angle is the key point and difficulty in the erection, but sometimes it is difficult to make the plane angle of the dihedral angle, or the plane angle is made, but the calculation is tedious. It can be found that the following formula can often be used to get rid of the above The dilemma. Theorem in Figure 1, tetrahedral P - ABC, PC surface ABC, ∠ PAC = α, ∠ BAC = β, dihedral angle P - AB - C size is θ, then tanθ = tanαsinβ.