A triangle has corners at points A, B, and C. Side AB has a length of 48 . The distance between the intersection of point A's angle bisector with side BC and point B is 9 . If side AC has a length of 36 , what is the length of side BC?

1 Answer
Nov 10, 2016

63/4

Explanation:

Call P the intersection point in the question.
Then using the sin theorem applied on triangles APC and APB we get

36/sin(AhatPC)=bar(PC)/sin(PhatAC)

48/sin(pi-AhatPC)=9/sin(PhatAB)

PhatAC=PhatAB\ \ \ by consdtruction and

sin(AhatPC)=sin(pi-AhatPC)

bar(PC)/36=sin(PhatAC)/sin(AhatPC)=sin(PhatAB)/sin(pi-AhatPC)=9/48

so

bar(PC)=9*36/48=9*3/4

and

bar(BC)=bar(BP)+bar(PC)=9+27/4=(36+27)/4=63/4