Answer: A
Step-by-step explanation:
Let the length side of the TV = a
The width of the TV = b
The diagonal of a TV = c
In a 30-60-90 right triangle,
We have cos(30°) = [tex]\frac{\sqrt{3}}{2}[/tex] and sin(30°) = [tex]\frac{1}{2}[/tex]
Given that c = 28 inches:
sin(30°) = [tex]\frac{b}{c}[/tex]
[tex]\frac{1}{2} = \frac{b}{c}[/tex]
[tex]b = \frac{1}{2} \times 28 = 14[/tex]
That is, the width of the TV = 14 inches
cos(30°) = [tex]\frac{a}{c}[/tex]
[tex]\frac{\sqrt{3}}{2} = \frac{a}{c}[/tex]
[tex]a = \frac{\sqrt{3}}{2} \times 28 = 14\sqrt{3}[/tex]
That is, the length of the TV = 14√3 inches
So the exact width and length of the TV are 14 inches and 14√3 inches.
Therefore, option A is the correct answer
