Given the lengths of two sides of a triangle, find the range for the length of the third side (between what two numbers should the length of the third side be). Write the inequalities for each case.

13.2 and 6.7

The length of the third side of given triangle lies between 6.5 and 19.9.

Step-by-step explanation:

The law of cosine is as follows

 ---------------1

⇒ a and b are the given sides of the triangle and c is the third side, and is the angle between a and b .

In equation 1 , the maximum and minimum values of are 1 and -1.

 so the value of c  lies in between

⇒ and     =

Given a=13.2 and b=6.7 so the the side lies in between  |13.2-6.7| and |13.2+6.7|

  so the third side lies between 6.5 and 19.9

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation:

29.5977692753

step-by-step explanation: