The figure shows △ABC.¯¯BD¯ is the angle bisector of ∠ABC. What is AD ?

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Answer 1 · 2017-01-10T16:56:34

2.67

In triangle ABC Tan B= #6/8#
Therefore angle B = #36.87degrees#

So angle ABD =#36.87/2= 18.43degrees#

Looking at triangle ABD
Tan 18.43=#(AD)/8#
AD=8x tan 18.43= 2.67

Answer 2 · 2017-01-10T17:47:55

#AD=2.67#

As #AD# is bisector of #/_A# from angle bisector theorem, we have

#(AD)/(DC)=(AB)/(BC)=8/10=4/5#

Hence we should divide #AC# in the ratio #4:5#

and hence #AD=4/(4+5)xx6=24/9=8/3=2.67#