the base of a triangle is 14 cm while the side ribs are 13 cm and 15 cm. Find the projections of the side ribs on the base

Question

this is a triangle with unequal sides

Answer 1

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.