Let
x-------> the length side of the TV
y-------> the width of the TV
d------> the diagonal of a TV
we know that
in a 30-60-90 right triangle
[tex]cos(30\°)=\frac{\sqrt{3}}{2}\\\\sin(30\°)=\frac{1}{2}[/tex]
[tex]d=26\ in[/tex]
[tex]sin(30\°)=\frac{y}{d}[/tex] ----> [tex]y=d*sin(30\°)[/tex]
[tex]cos(30\°)=\frac{x}{d}[/tex] ----> [tex]x=d*cos(30\°)[/tex]
substitute the values
[tex]y=26*\frac{1}{2}=13\ in[/tex]
[tex]x=26*\frac{\sqrt{3}}{2}=13\sqrt{3}\ in[/tex]
the length side of the TV is [tex]13\sqrt{3}\ in[/tex]
the width of the TV is [tex]13\ in[/tex]
therefore
the answer is the option A
13 inches by 13√3 inches
