Determine the length of the height of triangle ABC, that is perpendicular to BC, if BC= 15, AB=13 and AC=14.

We have the triangle ABC where
:

AB = 13 AC = 14 and BC =
15

Then we can find the area usind the
formula:

a =sqrt
P(p-a)(p-b)(p-c)

Forst let us determine
P

P = perimeter/2 = 13+14+15/2 = 42/2 =
21

==> a = sqrt(21*6*7*8) =
84

We also know that:

area (a)
= (1/2)* base*height

Since we need to determine the height
of the perpindicular on BC, then let the height be AD and the base is
BC.

==> a =
(1/2)*AD*BC

==> 84=
(1/2)*AD*15

==> AD = 84*2/15 =
56/5=11.2

Then AD = 11.2