My Math Forum Measuring Reflections

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 January 7th, 2012, 01:33 AM #1 Newbie   Joined: Jan 2012 Posts: 11 Thanks: 0 Measuring Reflections As in the image below, where on the left wall is the reflection point from the starting position, to object labeled "A." Moreover, if any of you gents are willing to explain in a way that an idiot can understand how to calculate this, I would appreciate it. FYI, this is for choosing the location of the door, on a wall I am building. If you wonder how it's relevant, I will be building acoustic panels and need to make sure they can go where I need. Thanks!
January 7th, 2012, 06:07 AM   #2
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Re: Measuring Reflections

[attachment=0:24w0q5ki]reflex2.jpg[/attachment:24w0q5ki]
Diagram is not to scale.

Angle A must equal angle B, so, by the tangent ratio,

x/48 = (108 - x)/110

5184 - 48x = 110x

5184 = 158x

x = 5184/158 = 2592/79, so the point on the left wall (where angle B is) should be 120 - 12 - 2592/79 = 5940/79 inches from the bottom wall.

Attached Images
 reflex2.jpg (14.9 KB, 159 views)

 January 7th, 2012, 10:26 PM #3 Newbie   Joined: Jan 2012 Posts: 11 Thanks: 0 Re: Measuring Reflections Thanks. How did you get 5184?
 January 8th, 2012, 01:37 AM #4 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond Re: Measuring Reflections x/48 = (108 - x)/110 48 * (108 - x) = 110x 5184 - 48x = 110x 5184 = 158x x = 5184/158 = 2592/79
 January 9th, 2012, 10:26 PM #5 Newbie   Joined: Jan 2012 Posts: 11 Thanks: 0 Re: Measuring Reflections Sorry mate, it does not make a bit of sense to me. .. Would you be willing to do one more for me? Same as above, however: I want to know where it hits the wall on the Right side, to get to A. (A is on the left.) Thanks!
 January 9th, 2012, 11:05 PM #6 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond Re: Measuring Reflections Sure, make the point on the right wall 1980/47 (about 42.13) inches from the bottom wall. Is there any way I can help you understand this?
 January 9th, 2012, 11:37 PM #7 Newbie   Joined: Jan 2012 Posts: 11 Thanks: 0 Re: Measuring Reflections Thanks for the answer, Greg. I finally figured out 5184, with the help of a chat room. You took the distance from left wall, and total of top wall minus distance from it (48 * 108 = 5184) And / 158 = distance from left wall plus total of top wall. Now I'm just trying to get it clear in my head how to add up those 3, distance from left wall, top wall, total top wall... when you change the scenario: i.e. the last problem. I should be able to figure it now though, hopefully. Thanks for your help.
 January 9th, 2012, 11:45 PM #8 Newbie   Joined: Jan 2012 Posts: 11 Thanks: 0 Re: Measuring Reflections Now that was just plain bad math on my part.. You took the distance to left wall for 110". My mistake. It makes much more sense now. I'll see if I can add it up.
 April 3rd, 2014, 04:08 PM #9 Global Moderator   Joined: Dec 2006 Posts: 20,968 Thanks: 2217 (1). Specify coordinates of the starting point (called S), reflecting wall and point A. (2). Calculate coordinates of B (reflection of A). (3). Calculate where the line SB intersects the reflecting wall. Last edited by skipjack; April 3rd, 2014 at 04:11 PM.

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