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# help geo

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A right triangle has side lengths 5, 12, and 13.  The angle bisector is drawn from the vertex with the right angle to the other side.  What is the length of the angle bisector?

Dec 9, 2020

### 3+0 Answers

#1
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Let AB  =12, BC  =13  and AC   = 5

Let the angle  bisector divide the  hypotenuse  into  segments x and  13 - x

And we have the  relationship

5 / x =  12/ ( 13 - x)

5 ( 13 -x)  = 12x

65  - 5x  = 12 x

65  = 17x

x =  65/17

And

sin 45  / (65/17)  =  sin BCA / bisector length

(1/sqrt (2)  / (65/17)  = ( 12/13)  /  bisector  length

bisector legth  =   (12/13) (65/17)  *sqrt (2)  =   (60/17)sqrt (2)   Dec 9, 2020
#2
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A right triangle has side lengths 5, 12, and 13.  The angle bisector is drawn from the vertex with the right angle to the other side.  What is the length of the angle bisector?

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Y = tan-1(3 / 12)              ∠X = 180 - (45 +∠Y)

AN / 12 = sin(Y) / sin(X)

AN = [12 * sin(Y)] / sin(X) = 4.991341987 Dec 9, 2020
#3
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corrections::::    ∠Y = tan-1(/ 12) jugoslav  Dec 9, 2020