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 Mar 15, 2021
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Triangle bisector theorem

 

12/AD = 15/DC            AC = sqrt 15^2 - 12^2 ) = 9     (Pythag theorem)

 

12/15  = AD/DC  

4/5    = AD/DC

                                AD = 4/9 * 9 = 4      DC = 5/9 *9 = 5

 

BD = SQRT (12^2 + 4^2)   = sqrt 160

 

Law of cosines:

 

15^2  =  5^5 + sqrt160^2-   2 * 5* sqrt160 cos BDC 

cos BDC = - .31623                   (if I made no mistakes....check my math !)

 Mar 15, 2021

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