Given:
BC is height of house that mean BC is perpendicular .
AB is base of triangle
AB = 10
AC is hypotenuse of triangle
AC = 12
Use Pythagorean theorem:
[tex]\text{hypotenuse}^2=perpendicular^2+base^2[/tex][tex]\begin{gathered} (12)^2=(BC)^2+(10)^2 \\ 144=(BC)^2+100 \\ 144-100=(BC)^2 \\ 44=(BC)^2 \\ BC=\sqrt[]{44} \\ BC=6.63 \end{gathered}[/tex]So the height of house is 6.63