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April 19th, 2019, 10:40 AM  #1 
Newbie Joined: Apr 2015 From: Lima Posts: 21 Thanks: 2  How to obtain projected areas with direction cosines?
Hello, I want to find a proof that shows that the projected areas of a plane with area (A) whose normal have direction cosines cos(Î±), cos(Î²), and cos(Î³), on the planes XY, XZ, and YZ are given by Az= A.cos(Î±) Ay= A.cos(Î²) Ax= A.cos(Î³) I found this proof but I have many Doubts about it: Designating as c the line common to triangles A1 and A in Figure 11.1c, the areas of Az and A are cb/2 and ca/2, where b and a are the altitudes normal to c of triangles A1 and A, respectively. So Az/A = b/a In figure 11.D we see that cos(Î±)=b/a. So Az/A = cos(Î±), and Az = A cos(Î±). How do I know that the altitudes "a" and "b" meet at point c? As far as I now that is true only for pyramids whose base are regular. How do I know if the normal that goes through the origin intersect the altitude "a"? Is there any other valid proof? BR Last edited by JoseTorero; April 19th, 2019 at 10:53 AM. 
April 24th, 2019, 09:48 AM  #2 
Newbie Joined: Apr 2015 From: Lima Posts: 21 Thanks: 2 
No one? 

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areas, cosines, direction, obtain, projected 
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