10.9 feet
Explanation:The diagram indicates a right-angled triangle
The value of h can be found by using the Pythagora's theorem
The pythagora's theorem states that the square of the hypotenuse is the sum of the squares of the other two squares
[tex]\begin{gathered} 12^2=5^2+h^2 \\ 144=25+h^2 \\ h^2=144-25 \\ h^2=119 \\ h=\sqrt[]{119} \\ h=10.9 \end{gathered}[/tex]The cat is 10.9 feet up the tree