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?
+128474 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)
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
