Determine the lenghth of the height in ABC triangle coresponding to BC side if AB = 13, BC = 15, AC = 14.

AB = 13, BC = 15 , Ac =
13.

So we use heron's formula to find the A area of ABC.
Then

A rea = (1/2)BC* h, where h is the altitude of the
triangle.

So h = 2*Area /BC  =
2Area/15...........(1)

Heron's formula for area  Area of
triangle = sqrt{s(s-a)(s-b)(s-c)}

Where s = (a+b+c)/2 =
(15+14+13)/2 = 42/2 = 21

Area =
sqrt{21(21-15)(21-14)(21-13)} = sqrt {21*6*7*8} = 84.

Use
this area 84 in  (1) to obtain h:

h = 2*84/15 =
11.2

Therefore the altitude from the side BC = 11.2
units.