A triangle has corners at points A, B, and C. Side AB has a length of 24 . 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 28 , what is the length of side BC?

1 Answer
Oct 26, 2016

28/24*4=14/3

Explanation:

Call alpha=hat A/2
Use the sin theorem twice on the 2 little triangles identified by bisector (call beta and pi-beta the angles opposite to bar(AC and bar(AB) in these triangles and remember that sin(beta)=sin(pi-beta))

x/sin alpha=28/sin beta

and

4/sin alpha=24/sin beta

substitute and obtain x=28/24*4=14/3