If ABC is the triangle, AB=14cm, AC=13cm, BC=15cm.
CD is the perpendicular from apex C on to base AB.
Cosine Rule:
BC²=AC²+AB²-2AC.ABcosA
225=169+196-364cosA
cosA=(365-225)/364=140/364=5/13.
AD (projection of AC on to AB)=13cosA=5cm.
Therefore BD (projection of BC on to AB)=14-5=9cm.