To find the length of the segment use the Pythagoras theorem below:
[tex]AC^2=AB^2+BC^2[/tex]
From the graph, we have:
AB = 15 - 3 = 12
BC = 7 - 2 = 5
Let's solve for the length of the segment AC:
[tex]\begin{gathered} AC^2=12^2+5^2 \\ \\ AC^2=144+25 \\ \\ AC^2=169 \end{gathered}[/tex]
Take the square-root of both sides:
[tex]\begin{gathered} \sqrt[]{AC^2}=\sqrt[]{169} \\ \\ AC\text{ = 13} \end{gathered}[/tex]
Therefore, the length of this segment is 13
ANSWER:
13
