The Law of Sines only find unknowns in oblique triangles. Oblique triangles are triangles that have no right angles.
The Law of Sines can be derived from an oblique triangle, by drawing an altitude from any side(h).
Using sine trigonometry you can break the triangle into two parts.
1.
2.
Now,it is possible to substitute for h. In order to have a trigonometry h needs to be eliminated.
Divide each side by c
Since you can draw an altitude from any of the sides all of the proportions are equal.
Example:
To find the area one can derive the equation from an oblique triangle with an altitude.
Since the altitude can be drawn from any side, the Area formula can change as long as it uses two sides and the included angle. Here are some other forms:
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