Hello there. To solve this question, we'll have to remember some properties about the triangular inequality.
Given the following triangle in which the buses A, B and C are its vertex:
We know that Bus C is 8 miles away from bus B and bus C is 23 miles away from bus A.
We want to determine the possible distances between the buses A and B.
For this, remember the triangular inequality:
For any three sides of a triangle, say x, y and z, the biggest side z has to satisfy
[tex]z\leq x+y[/tex]
So we're able to find an inequality that gives us the possible sides of the triangle, and, hence, the distances between the buses.
Plugging x = 8 and y = 23, we get
[tex]\begin{gathered} z\leq8+23 \\ \\ \\ \end{gathered}[/tex]
Also, z has to be greater than or equal to 23, since it is the biggest side, therefore
[tex]23\leq z\leq31[/tex]
So the possible values we can choose from the options are between 23 and 31.
These are the answers in this case: 23, 25, 27 and 30
