Advanced trigonometry of Non Right Angle Triangles

 Trigonometry revolves around finding the length/ angle of a part of a triangle using various methods. One can use the basic formulas to find the values of a right angled triangle but we can use other formulas for non-right angled triangles.




Important Formulas: 


This formula is used to find the area of any triangle ↑


In all of these formulas, the uppercase letters represent the angle and the lowercase letters represent the side opposite to the corresponding angle.


Now let's work with a question!

We can first use the cosine rule to find one the angles.
Let us start by finding out the value of the angle opposite 6.5cm. 

So we use the cosine rule, and substitute the values:
a=6.5
b=4.3
c=5.2
and cosA is unknown. 
We make cosA the subject of the formula and solve. Then we find A using the inverse cos.
A= 85.8

Now we have an angle and a side. We can use the sin rule to find the rest of the angles:
sin85.8/6.5=
sinB/4.3=
sinC/5.2

We get the values of the angles as
A=85.8
B=41.3
C=52.9
The angles add up to 180!

We can further use these values to find the area of triangle ABC using formula 2. 
The answer should be 11.15!



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