The diagonal of a tv is 30 inches long. assuming that this diagonal forms a pair of 30-60-90 right triangles, what are the exact length and width of the tv?

The ratio of sides for a 30 : 60 : 90 =  1 : √3 :2.

Note the 90 degrees represent the hypotenuse, which in this case is 30 inches.

1 : √3 :2 =  x : y : 30

To get 1, on the left side, we simply divide 2 by 2

Similarly x = 30/2 = 15.

To get √3, on the left side, we simply multiply 1 by √3

Similarly y = 15 * √3 = 15√3

Therefore the length and width respectively are 15 and 15√3 inches