借助空间向量,很容易推导出二面角有以下两个计算公式.(1)如图1,AB、AC、AD是空间自A引出的三条射线,所成角分别为θ1,θ2和θ,可求得二面角B-AC-D的大小(用θ1,θ2和θ的三角函数表示)解:作BC⊥AC于C,DE⊥AC于E,图1则BC和DE夹角度数即为二面角B-AC-D度数.设AB=a,AD=b.BC=BA+AC With space vectors, it is easy to deduce that the dihedral angle has the following two calculation formulas. (1) As shown in Fig. 1, AB, AC, and AD are three rays radiating from A in space, and the angles formed are θ1, θ2, and θ, respectively. The size of the dihedral angle B-AC-D (expressed as a trigonometric function of θ1, θ2, and θ) can be obtained as follows: BC ⊥ AC in C, DE ⊥ AC in E, and Figure 1 shows the number of BC and DE angles Dihedral B-AC-D degrees. Let AB=a,AD=b.BC=BA+AC