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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(α), cos(β), and cos(γ), on the planes XY, XZ, and YZ are given by Az= A.cos(α) Ay= A.cos(β) Ax= A.cos(γ) 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(α)=b/a. So Az/A = cos(α), and Az = A cos(α). 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?  Tags areas, cosines, direction, obtain, projected Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Statistics132 Applied Math 0 March 21st, 2017 11:55 AM markosheehan Applied Math 2 November 26th, 2016 10:24 AM bigyan1einstein Geometry 0 April 17th, 2016 07:22 PM keystone Economics 1 July 6th, 2012 07:14 PM konkeroc Algebra 0 April 27th, 2011 07:26 AM

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