The Law of Sines can be used to find unknown parts (a side or angle) of a triangle. For example if you know 2 angles and a side, or if you know 2 sides and 1 angle (depending on how they are oriented). Visit the Maths Is Fun site (link posted below) for a more graphical explanation.
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The tricky part of the law of sines is knowing when you are able to use it. Whether you can use the law of Sine's or not depends on what information you have or were given. In some cases the information you were given could make two different triangles. There are three times when you can use the law of sines. One example of when you can use it is when you have the length of a side and the measures of both the angles that that side is adjacent to. This is called angle side angle or asa for short. Another time when you can use the law of sines is when you are given the measures of two angles and a side that is outside the angles. This is called aas. Finally the last case where you can use the law of sines is when you have two side lengths and the measure of an angle. Math teachers refer to this one as ssa, I remember that this one is special. If you are given the measure of an angle and two sides you could have two different triangles.
When none of the angles are known, and using Pythagoras, the triangle is known not to be right angled.
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SinA/a = SinB/b = SinC/c
In trigonometry sines and cosines are used to solve a mathematical problem. And sines and cosines are also used in meteorology in estimating the height of the clouds.