Students often show their interest on mathematics and this would include geometry and trigonometry. This is the reason why it becomes vital to understand different aspects of subject. While getting into depth of law of sines you will understand that it is formula related to the sides along with angles of triangle. It is the formula which would enable to find side length of angle of triangle.
In case of ΔABC, you need to know that ΔABC is oblique triangle and each of its side is determined as a, ba, b and cc
a             b             c
——–  =  ——–  =  ——–
sinA        sinB         sinC
Reasons to use it and why it is used
You should probably know that a triangle consists of three sides which are why it also has three angles. Therefore, law of sines is a tool which helps to find a solution for triangle. For example, if six measures are mentioned, then it is possible to find out the rest. But, this would again depend on what you are actually given and so this tool can be adopted to combine with any other formula to complete triangle.
When to use the law of sines?
The law of sines can certainly be used only when you know:

  1. One side and therefore its opposite angle
  2. One or more sides or angles

This is when it is possible to calculate “Law of Sines” and ratio s.
State whether the given measurements determine zero
It has been already discussed that to make use of law of sines it is essential to have knowledge either of two angles or one side of triangle (AAS or ASA) or even any other two sides of angle which is opposite to one of them (SSA).
Understand it with an example

  • State whether the given measurements determine zero, one, or two triangles. a = 80°, a = 24, b = 50

Solution: sin 80° = x
x = 50 sin 80° » 49.2
Because a<x and so no triangle is formed
Angle side angle (ASA) or side angle angle (SAA)
If we are aware of two different measurements of angles, then it is quite convenient to find out the measurement of third angle as it helps to measure angle of any triangle which can add up to 180°. This is when it is possible to make use of sines.
Side by side angle
In case two sides you are aware of and then an angle, then there are three different possibilities. Sometimes, you might find that there is only 1 triangle that carries information. There are other two possibilities which would fit data and so the data available would create an impossible situation.
It is important to state whether the given measurements determine zero, one, or two triangles. a = 80°, a = 24, b = 50. But, you can’t possibly say that law of sines can always help to solve the problem of triangle. With two known side and measurement of angle, there is less possibility of using law of sines which would further help to solve triangle as there is no pair of any opposite angle which can enable to measure.
You can possibly get help from the professionals to understand trigonometry and understand the law in depth.

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