A triangle has corners at points A, B, and C. Side AB has a length of #9 #. The distance between the intersection of point A's angle bisector with side BC and point B is #4 #. If side AC has a length of #15 #, what is the length of side BC?
1 Answer
Explanation:
The bisector of an angle of a triangle divides the opposite side of the triangle into two segments whose ratio is the same as the ratio of the triangle's sides of the bisected angle.
In the diagram below,if
Given:
we have
In case you have not been given the ratio rule used above,
here is a quick proof of why it is true.
Draw a line parallel to
SInce
Furthermore since
Therefore