Question 364269
I would use the pythagorean theorem to solve this problem. 
Since televisions are measured diagonally, you have a right triangle. 
Our hypotenuse is 10 and we will consider the width {b=8}. 
Our unknown is a.

(a^2)+(b^2)=(c^2)
So we have (a^2)+(8^2)=(10^2)

(a^2)+64=100

(a^2)+64-64=100-64

(a^2)=36

Now we will take the square root of 36, and it happens to 
be a perfect square so there are 2 solutions = (-6, 6) 
Since -6 is not a possible length, we will throw out that solution. 

Answer, the height is 6 inches.