Question 234082
This problem is done using the Pythagoran theorem. Which says that {{{a^2+b^2=c^2}}}
This says that the two shorter sides of a right triangle squared equal the long side squared
{{{drawing( 300, 300, -15, 15, -15, 15, 
         grid(1),
red(triangle( 0, 0, 0, 9, 12, 0 )),
green(rectangle(12,0,0,9,0,0,12,9))          
          
)}}}
And the triangles longest side is the diagnol line across the tv set.
So we know the diagnol of the tv is 15, so {{{c=15}}}
And we know the leangth is 12 so {{{a=12}}}
This gives you that {{{15^2=12^2+b^2}}}
{{{225-144=b^2}}}
{{{b^2=81}}}
{{{b=9}}}
Since b is the height of your triangle the height is 9.