Hello there. To solve this question, we'll have to remember some properties about triangles.
Given the triangle with sides x, y and z as follows:
It obeys the following inequality:
[tex]x+y>z[/tex]This is called the triangle inequality.
In this case, we can plug the given sides of the triangles and determine the range of possible measures for the third side using this inequality.
In fact, we only need that this third side has a measure bigger than zero (because we're talking about a geometrical figure).
Solving each question:
17) 27, 33
Plugging the values, we get:
[tex]\begin{gathered} 27+33\ge z \\ 50>z>0 \end{gathered}[/tex]Therefore the range of the possible values for the third side of the triangle is given by:
[tex](0,50)[/tex]18) 37, 32
Plugging the values,
[tex]\begin{gathered} 37+32>z \\ 69>z>0 \end{gathered}[/tex]And the range is given by:
[tex](0,69)[/tex]19) 25, 47
Plugging the values,
[tex]\begin{gathered} 25+47>z \\ 72>z>0 \end{gathered}[/tex]And the range is given by:
[tex](0,72)[/tex]20) 46, 37
Plugging the values,
[tex]\begin{gathered} 46+27>z \\ 73>z>0 \end{gathered}[/tex]And the range is given by:
[tex](0,73)[/tex]==
Given a triangle with the following angles:
