This will use trigonometric ratios (sin, cos, tan). First, use 16 and 9 as the sides of your tv. Now let's look at the angle opposite the 9. Using the tangent ratio, we can tell that the Wine of the angle is equal to 9/16, making the angle 29 degrees, and the third angle 61 degrees. Now that we know the angles, we can use the angles and the side we know to find the value of the missing sides. The dimensions will end up being 29.4 x 52.3.
Use the Pythagorean Thm to find the diagonal (hypotenuse) of the small 9 by 16 rectangle. It will have a decimal. Lets call that "c". Now draw a similar bigger rect. that has a diagonal of 60. To find the width, set up a prop: c/60 = 9/width. Solve for w. do the same thing for length. c/60 = 16/ length