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

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?

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.

According to the notation in the figure:

http://www.vbforums.com/attachment.p...chmentid=18935

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}

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.

Quote:

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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.

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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.

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.