Mathematics: The diagonal of a tv is 26 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? a. 13 inches by 13√3 b. 13√2 inches by 13√2 inches c. 52√2 inches by 52√2 inches d. 52 inches by 52√3 inches

X/2 = 1.25 x is your allowance...

The diagonal of a tv is 26 inches long. assuming

aredding7016

17.01.2022

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

$cos(30\°)=\frac{\sqrt{3}}{2}\\\\sin(30\°)=\frac{1}{2}$

$d=26\ in$

$sin(30\°)=\frac{y}{d}$ ----> $y=d*sin(30\°)$

$cos(30\°)=\frac{x}{d}$ ----> $x=d*cos(30\°)$

substitute the values

$y=26*\frac{1}{2}=13\ in$

$x=26*\frac{\sqrt{3}}{2}=13\sqrt{3}\ in$

the length side of the TV is $13\sqrt{3}\ in$

the width of the TV is $13\ in$

therefore

the answer is the option A

13 inches by 13√3 inches

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