Triangle half-angle formulas express the sine, cosine, and tangent of half an angle
of a triangle in terms of its side lengths. Let 
, 
,
and 
be the lengths of the sides opposite angles 
, 
,
and 
, and let 
be the semiperimeter.
Applying the half-angle formulas to the law of cosines gives
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
Substituting 
in the triangle
area formula 
gives Heron's formula
(José García 2020).
