Cosine theorem . In Geometry and more specifically in Euclidean geometry , it is a trigonometry theorem that in each triangle indicates the relationship between the proportion of the sum and the difference of the lengths of two sides with the tangents of half the amplitudes of the Add and subtract the angles opposite those sides.
Summary
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- 1
- 2 Implications and importance.
- 3 See also.
- 4
Definition.
Let any triangle be like the one in the figure:
The tangent theorem states that the sum of the lengths of two sides is the difference of those two sides as the tangent of half the total amplitude of the angles opposite to those sides is the tangent of half the difference of these angles.
Or what is the same:
Implications and importance.
The tangent theorem plays a very important role in the calculation and definition of surfaces and volumes that can contain triangles. Together with the triangular inequality , the sine and cosine theorem, allow a characterization of the constituent elements (the lengths of the sides and amplitudes of the interior angles of the triangles), so that it can first be distinguished that they make up a triangle and in addition, their relationship with their angles, among many other properties.
