Question 143958
An {{{altitude}}} of a triangle is a straight line through a vertex and perpendicular to ( forming a right angle with) the opposite side. This opposite side is called the base of the altitude.

The length of the {{{altitude}}} is the distance between the base and the vertex.

Calculating the area of a triangle is an elementary problem encountered often in many different situations. 

The best known, and simplest formula is: {{{S=(1/2) bh}}}
where {{{S}}} is area, {{{b}}} is the length of the base of the triangle, and {{{h}}} is the height or altitude of the triangle. 

If you know the area, you can calculate the height or {{{altitude}}} like this:

{{{S=(1/2) bh}}}……..solve for {{{h}}}
{{{2S=bh}}}
{{{h=2S/b}}}

Right Triangle Altitude: The measure of the {{{altitude}}} drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse.
In terms of our triangle {{{ABC}}}, this theorem simply states what we have already shown: 

if the altitude has intersection point {{{D}}} with a hypotenuse, then 

{{{AD= sqrt(CD*DB)}}}

since {{{AD}}} is the {{{altitude}}} drawn from the right angle of our right triangle to its hypotenuse, and {{{CD}}} and {{{DB}}} are the two segments of the hypotenuse.