It's been awhile since I was in Geometry...

[The Hobo]

If I know the length of all three sides of a triangle, is there a way that I can compute the height so that I might get the area?

And the base would be the longest side, correct?

[opus]

I had the same problem (the reason was thread '213977 from SilverSprite ;-) )
I used the following link :"http://www.mathe-aufgaben.de/mathehilfen/mathe-abitur/Trigo/16201%20LEBLA%20Trig%20nrw%20Dreiecke.pdf"
Sorry,it's in German, but you should be able to use the formulas.
Your problem is SSS, that is 3 sides(S) are known, have fun.
If you need some translation, just yell.

[krtxmrtz]

According to the notation in the figure:



a = m + n
h² = b² - m²
h² = c² - n²

n = a - m which is substituted into the third of the above equations. Then, the last 2 equations yield:

h² = b² - m²
h² = c² - (a - m)²

I now substract these 2 from one another:

c² - a² -m² + 2am - b² + m² = 0

from which,

m = (a² + b² - c²) / (2a)

and finally:

h = Sqr{ b² - [(a² + b² - c²) / (2a)]²}

[Kalkewl8ter]

You can find the area first, and then compute the height from it, by using Heron's formula, which states that the area of any triangle is:

sqrt(s*(s-a)*(s-b)*(s-c))

such that a, b, and c are the sides, and s is the semi-perimeter of the triangle, which can, of course, be found from knowing the side lengths. Find the area and substitute it into A=b*h/2, and you can easily find the altitude from any side.

[The Hobo]

Originally posted by Kalkewl8ter
You can find the area first, and then compute the height from it, by using Heron's formula, which states that the area of any triangle is:

sqrt(s*(s-a)*(s-b)*(s-c))

such that a, b, and c are the sides, and s is the semi-perimeter of the triangle, which can, of course, be found from knowing the side lengths. Find the area and substitute it into A=b*h/2, and you can easily find the altitude from any side.

I actually forgot about Heron's formula, but remembered it last night. I don't actually need to know the hight, just the area. The formula works perfect for it.

[bugzpodder]

another way is use cosine law to find one of the angles, then simply solve for the height. accroding to krtxmrtz's diagram, find the angle C (between length a and b) and then do bsinC for the height. or you can go directly to the area formula absin(t)/2 where t is the angle between a and b, but note that bsin(t) is the height.