Given a 5-12-13 right triangle, find the length of the angle bisector from the right angle to the hypotenuse.
+128475 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
