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Given a 5-12-13 right triangle, find the length of the angle bisector from the right angle to the hypotenuse.

 Feb 20, 2020
 #1
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See the following :

 

 

Let  AD   be the bisector....and this sets up the following relationship 

 

 AC / AB   = CD / BD

 

12/ 5  = CD/ BD

 

 

Thus  there are  (12 +5)  =  17 equal parts  to BC  so  CD  is (12/17) *13  =  156/17

 

And angle DAC  = 45°

 

And the sin  of angle BCA  = 5/13

 

So....using the Law of Sines

 

CD  / sin DAC  =  AD  /sin (BCA)

 

156/17 / sin (45)  = AD  / (5/13)

 

(156/17) (5/13) √2  = AD  =  60√2  / 17  ≈  4.99

 

 

cool cool cool

 Feb 20, 2020

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