Mr lee buys a 30-inch television.the height of the screen is 18 inches. given that television screens are measured across the diagonal,i.e. the length of the diagonal is 30 inches, how wide is the screen?

30-18 = 12

The width of the screen is >= 12

The answer is:  " 27.5 inches " .

The width of the television set is:  "27.5 inches" .

Explanation:

To find the "width"; we use the "Pythagorean theorem" ; 

which is:  a² + b² = c² ;
 
in which "c" refers to the "hypotenuse" or "diagonal" (of this "right triangle" that is formed;  We are given:  " c = 30 in" 

in which "a" and "b" represent the lengths of each of the other two (2) sides of the right triangle.

Since we are given that the "height" of the TV is 12 in. 

Let "b = 12 in".

We are trying to solve for the "width".

Let "a" represent the width (in inches"; 

So, we are trying to solve for "a" (the width):

Plug in our known values:

a² + 12² = 30² ; and solve for "a" ; 

Rearrange the equation:

a² = 30² − 12²    ;

Take the "positive" square root of each side of the equation; to solve for "a" ;

+√(a²) = +√(30² − 12²) ;

   a = +√900 − 144)

   a = +√756 ;

   a =   27.49545416973504 ;  round to:  27.5 ;

The answer is:  " 27.5 inches " .

The width of the television set is:  "27.5 inches" .

The answer is:
D)  cos(60°) = a/12