Question

answer step wise .......

Answer 1

when you apply the cosine theorem

the data that you have to introduce is:

side AB = 4,

side BC = 6

Side AC = sqrt (AB^2+BC^2–2AB*BC*cosine (angle between AB and BC)

angle between AB and BC= 0 and 180, because I pretend to evaluate all the possible triangles that can be created, after

Then you will get a lot of possible triangles, you just have to change the angle between AB and BC

and the values of the third side range from 2 to 10, as you may notice, the superior and inferior limits is no more than the difference and the sum of both sides.
I hope u can understand now

Answer 2

The sum of two side of triangle=4+9=13

Therefore the third side of triangle should be less than 13

the difference of two side of triangle

= 9-4 =5

therefore the third side of triangle

should be more than 5

so we can take here 6;7;8;9;10;11;12 as third side of triangle

Here we are taking 6 as the third side of triangle

=a+b>c

=4+6=10 >9