Answer:
The vertical height is [tex]h=3\ units[/tex]
Step-by-step explanation:
we know that
In the right triangle ABC
see the attached figure
To find the height h apply the Pythagoras Theorem
[tex]c^{2}=a^{2}+b^{2}[/tex]
we have
[tex]c=AB=3\sqrt{2}\ units[/tex]
[tex]a=BC=6/2=3\ units[/tex]
[tex]b=AC=h\ units[/tex]
substitute
[tex](3\sqrt{2})^{2}=3^{2}+h^{2}[/tex]
[tex]18=9+h^{2}[/tex]
[tex]h^{2}=18-9=9[/tex]
[tex]h=3\ units[/tex]
