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May 12th, 2015, 02:53 AM  #1 
Newbie Joined: May 2015 From: england Posts: 1 Thanks: 0  Need Help Finding the lengths.
Hi all, I'm so stuck on this question, can you help me find the lengths and include the workings out? 
May 12th, 2015, 01:42 PM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,574 Thanks: 667 
You haven't shown what you have tried or told us what you do know about this, so I don't know if this method is reasonable for you, but here is how I would do it: Set up a coordinate system with point F at the origin, the xaxis along GE and the yaxis along FB. Then A has coordinates (13, 3.2), E has coordinate (13, 0), and B has coordinates (0, 10). The distance from $\displaystyle (x_0, y_0)$ to $\displaystyle (x_1, y_1)$ is $\displaystyle \sqrt{(x_1 x_0)^2+ (y_1 y_0)^2}$. Once you have found the length of AE and BE, as asked, do the same thing to find the length of AB so that you know all three sides of triangle ABE. The angle AEB can be gotten from the "cosine law": $\displaystyle AB^2= AE^2+ BE^2 2(AE)(BC)\cos(AEB)$. Last edited by skipjack; May 12th, 2015 at 11:49 PM. 
May 13th, 2015, 08:03 PM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,098 Thanks: 683 
Calculate BE from right triangle BEF (EF = 13, BF = 10). Calculate AE from right triangle AEG (GE = 26, AG = 3.2) Calculate AB from right triangle ABM (AM = 13, BM = 103.2 = 6.8) Use Cosine Law to calculate angle AEB. 

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finding, lengths, triganometry 
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