A triangle has corners at points A, B, and C. Side AB has a length of #36 #. The distance between the intersection of point A's angle bisector with side BC and point B is #8 #. If side AC has a length of #42 #, what is the length of side BC?

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Answer 1 · 2016-09-16T03:17:27

#17.3333#

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Let the intersection point be D (see diagram)

Using Laws of sine :

a) triangle ABD

#36/siny=8/sinx => sinx/siny=8/36 = 2/9# ----- (1)

b) triangle ADC

Let E be the distance between D and C

#42/sin(180-y) = E/sinx#

Recall that #sin(180-y)=siny#

#=> E/42 = sinx/siny# --- (2)

Eq (1) = Eq (2)

#=> E/42 =2/9#

#=> E = (42xx2)/9 =9.3333#

Length of BC #= 8+9.3333=17.3333#