triangle
If now A, B, and C denote the angles of the triangle, and a, b, and c the lengths of the sides opposite them, the following results hold:
Proving the angle sum formula
Determining the area of a triangle
(i) The area of the triangle equals 
.
.(ii) The sine rule:
where R is the radius of the circumcircle.
(iii) The cosine rule:
(iv) The tangent rule:
(v) Hero's formula: Let 
. Then the area of the triangle equals
. Then the area of the triangle equals
See acute, obtuse, oblique, equilateral, isosceles triangle, right-angled triangle, scalene triangle, solution of triangles, spherical triangle.
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