High school mathematics: very practical derivation of space cosine theorem and analysis of examples

2022-05-28 0 By

We often meet the problem of calculating the Angle or cosine of Angle of a line with different plane in solid geometry.The solutions are often :(1) translation to the same plane and then use the knowledge of plane geometry to solve;(2) Use space vectors.But what we’re going to do today is use the law of cosines in space to solve that problem.Straight lines in different planes included Angle cosine (set straight lines in different planes AB an Angle of theta, CD) : by the above inference formula we can see that we only need according to the conditions, expressed or and closely related with conclusion asked the four points of the length of each tetrahedron, and then the generation of edge into the formula to the appropriate location, you can get the conclusion we need.To get your child interested in math, read this book:As shown in the figure, in the straight triangular prism ABC-A1b1C1, Angle BAC=π/2, AB=AC=AA1=2, points G and E are the midpoints of line segment A1B1C1C respectively, points D and F are moving points on AC and AB respectively, and GD orthogonal EF, then the minimum value of DF of line segment is?Example 2: As shown in the figure, in the triangular pyramid A-BCD, AB=AC=BD=CD=3, AD=BC=2, points M and N are the midpoints of AD and BC respectively, then the cosine value of the Angle formed by the heteroplane lines AN and CM is ().Well, today’s content is shared here, if you have any questions, you can leave a message below the article, welcome to continue to pay attention to, wonderful will continue!