you can find the height using Pythagorus. If you think of the TV screen as a rectangle, cut that rectangle in half from one corner to another.

You would then have a right angled triangle, the diagonal of that would be the hypotenuse which is given(10 inches) the width would be one of the other two sides (8 inches) The height would be the remaining side which we can find using Pythagorus

we know the hypotenuse is 10 so therefore c=10 and one side is 8 so say a=8 and we want to find b (which would be the height)

rearranging that we have

so