Is there a way to find the area of a triangle by only knowing the lengths of each side? I have been trying to find a way (and am almost done) I would just like to know if this has been solved before...
Is this what you mean?
Heron's Formula -- from Wolfram MathWorld
Hello, Quick!
Is there a way to find the area of a triangle by only knowing the lengths of each side?
I have been trying to find a way (and am almost done).
I would just like to know if this has been solved before.
Yes . . . a long time ago . . .
Heron's Formula
If a, b, c are the sides of the triangle and s = (a + b + c)/2, the semiperimeter,
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then the area is given by: . A . = . √s(s - a)(s - b)(s - c)
Given a triangle with sides a, b, and c and angles A, B, and C across from that side (respectively) (ie. angle A is across from side a, etc.)
Law of Sines:
a/sin(A) = b/sin(B) = c/sin(C)
Law of Cosines:
a^2 = b^2 + c^2 - 2bc*cos(A)
b^2 = a^2 + c^2 - 2ac*cos(B)
c^2 = a^2 + b^2 - 2ab*cos(C)
(Notice the pattern.)
(Note also that the Law of Cosines is a generalization of the Pythagorean Theorem to a triangle that is not a right triangle.)
-Dan