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

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### 2 Answers

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.

We'll write the formula for the area of a triangle:

A = (BC*h)/2, BC is the base of the triangle and h is the height.

In this formula we know the length of BC=15, but we don't know the value of the area.

We'll determine the area using Heron's formula:

A = sqrt (p(p-a)(p-b)(p-c)), where p is half-perimeter of the ABC triangle.

p = (a+b+c)/2=(AB+AC+BC)/2=(13+14+15)/2=21

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

A = sqrt (p(p-AB)(p-AC)(p-BC))

A=sqrt (21(21-13)(21-14)(21-15))=84

84 = (BC*h)/2=(15*h)/2

h=(2*84)/15

**f = 56/5**