Law of Sines

Let us study about Law of Sines,
You can use the Law of Cosines discussed in the last section to solve general triangles, but only under certain conditions. The formulas that will be developed in this section provide more flexibility in solving these general triangles.

The following discussion centers around Figure 1 .
Figure 1

Reference triangles for Law of Sines.

Line segment CD is the altitude in each figure. Therefore Δ ACD and Δ BCD are right triangles. Thus,


In Figure 1 (b), ∠CBD has the same measure as the reference angle for β Thus,
It follows that


Similarly, if an altitude is drawn from A,


Combining the preceding two results yields what is known as the Law of Sines.
In other words, in any given triangle, the ratio of the length of a side and the sine of the angle opposite that side is a constant. The Law of Sines is valid for obtuse triangles as well as acute and right triangles, because the value of the sine is positive in both the first and second quadrant—that is, for angles less than 180°. You can use this relationship to solve triangles given the length of a side and the measure of two angles, or given the lengths of two sides and one opposite angle. (Remember that the Law of Cosines is used to solve triangles given other configurations of known sides and angles).

First, consider using the Law of Sines to solve a triangle given two angles and one side.
Hope the above explanation was helpful.