A triangle has corners at points A, B, and C. Side AB has a length of #21 #. The distance between the intersection of point A's angle bisector with side BC and point B is #5 #. If side AC has a length of #18 #, what is the length of side BC?
1 Answer
Feb 11, 2017
Explanation:
Let D be the point on BC where the angle bisector, intersects with BC
Then BC = BD+ CD
We know that BD = 5 and have to find CD
Using the
#color(blue)"Angle bisector theorem"# on this triangle.
#color(red)(bar(ul(|color(white)(2/2)color(black)((BD)/(CD)=(AB)/(AC))color(white)(2/2)|)))# Substituting known values into this equation.
#rArr5/(CD)=21/18#
#color(blue)"cross multiply"#
#rArr21CD=5xx18#
#rArrCD=90/21=30/7=4 2/7#
#rArrBC=5+4 2/7=9 2/7#