Question 176129
A triangle has vertices S(0,7), E(5,-6), and T(10,7). Find the length of the altitude to the shortest side.
<pre>
{{{drawing(400,400,-3,12,-7,8,locate(0,7.7,"S(0,7)"),locate(10.3,7.7,"T(10,7)"),locate(4.5,-6,"E(5,-6)"), 

graph(400,400,-3,12,-7,8), triangle(4.7,-6,10,7,0,7))}}}

The altitude is a vertical line through E, so it has to 
have the same x-coordinate as E, that is, 5, and it is on 
the same level as S and T, so it has the same y-coordinate
as S and T, that is, 7.  

So we draw in the altitude EA(5,7):

{{{drawing(400,400,-3,12,-7,8,locate(0,7.7,"S(0,7)"),locate(10.3,7.7,"T(10,7)"),locate(4.5,-6,"E(5,-6)"), line(5,-6,5,7),
locate(4.9,7.7,"A(5,7)"),
graph(400,400,-3,12,-7,8), triangle(5,-6,10,7,0,7))}}}

So the altitute extends 6 units below the x-axis and 7
units above the x-axis, so the altitude EA is 6+7 or 13 
units in length

Edwin</pre><b>