April 4th, 2008, 07:04 PM  #1 
Newbie Joined: Apr 2008 From: Alabama Posts: 2 Thanks: 0  I'm Stumped
I want to solve the following equation for b: (b*r)^2 + b^2 = c^2 This equation is similar to the Pythagorean theorem, except that "a" is replaced with "b*r", r being a ratio. I have wasted 5 sheets of paper trying to solve for b, to no avail. If you assume: c = 10 and r = 4/3 Then "b" should yield 6. I feel stupid. Thanks. 
April 4th, 2008, 07:58 PM  #2 
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3 
(b*r)^2=(b^2)*(r^2) because exponents distribute over multiplication. so: (b*r)^2+b^2=c^2 b^2*r^2+b^2=c^2 (r^2+1)(b^2)=c^2 And you should be able to take it from there. Cheers. 
April 5th, 2008, 08:33 AM  #3 
Newbie Joined: Apr 2008 From: Alabama Posts: 2 Thanks: 0  thanks, got it
Thanks for the tip. I finished up and solved for b. b = sqrt( c^2 / ( r^2 + 1 ) ) I need to read up on my math rules. I'm going to use this formula in a software program that calculates the viewable screen area and DPI resolution of LCD Monitors given the diagonal measure and native screen resolution. I can get the ratio ("r") of any display by dividing the horizontal resolution ("x") by the vertical ("y") and using the diagonal measure ("c") I can determine the height ("b") and width ("b*r") of the monitor and multiply them together to get screen area. And to get DPI, I just use: dpi = sqrt( x^2 + y^2 ) / c I just thought you might me interested in what the formula was for. Thanks for your help. 
April 5th, 2008, 12:46 PM  #4 
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3 
Yeah those rules are things that become intuitive after a while... but it's really easy to forget that they're intuitive... unless you work with set theory or higher algebra, where they aren't guaranteed... Anyway, that's a clever way of handling screen resolution. I assume everything is going to be scaled to fit the screen properly? I suddenly remember why I stick with theoretical CS... 
April 5th, 2008, 01:15 PM  #5 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  Re: I'm Stumped
(br)² + b² = c² = b²r² + b² = b²(r² + 1) b² = c² / (r² + 1) b(c,r) = ±c / √(r² + 1), where the function is in two variables. b(10, 4/3) = ±10 / √(16/9 + 1) = ±10 / (5 / 3) = ±6 

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