立体几何中 ,角的研究包括异面直线所成的角、直线和平面所成的角和二面角 .传统方法是通过“作、证”转化为在三角形中求平面角 ,而高中数学教材 (第二册下B)则通过向量工具 ,把求角问题转化为用cosθ =a·b｜a｜｜b｜来计算 ,大大降低了思维的难度 ,充分体现了几何问题代数化 In the three-dimensional geometry, the study of the angle includes the angle formed by different straight lines, the angle formed by the straight line and the plane, and the dihedral angle. The traditional method is to transform the plane angle in the triangle by “work and witness”, and the high school mathematics textbook (Volume 2 in B) uses the vector tool to convert the angle finding problem into cosθ = a·b|a||b|, which greatly reduces the difficulty of thinking and fully reflects the algebraization of geometric problems.