Question 714837: I have right triangle that I need to know the 2 legs
hypotnues is 22 what are the legs.
the second thing is i need the middle height of the triangl after the legs are found
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! You need more information, because there is an infinite number of triangles with a hypotenuse of 22.
There is probably some other information that you are missing (problem not properly copied), or you are not noticing some given information.
Maybe you are given some information about the measure of the angles.
Maybe there is some information about how the lengths of the sides are related.
If you were told that is is a isosceles right triangle, you would know that the two legs have the same length.
The could be information hidden in a drawing:
There could be identical marks on the legs,indicating that they have the same length.
There could be identical arcs on the acute angles, indicating that they have the same measure.
If you were given a drawing that labels the legs as some expression with x (like 2x+3), that could be useful information.
Once you have the length of all 3 sides, you can calculate your altitude to the hypotenuse, as
Consider the two congruent triangles below.
 (They are the same triangle, just flipped and rotated).
For the triangle on the right you would calculate the area as
 , specifically 
For the triangle on the left you would calculate the area as
 , specifically 
But the triangles are the same and so are the areas, so
 -->  --> 
With numbers:
 -->  --> 
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