desalviniprin8ce
contestada

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?. A. 15 inches by 15/3 inches. B. 15/2 inches by 15/2 inches . C. 60 inches by 60/3 inches . D. 60/2 inches by 60/2 inches

Respuesta :

13ray23
A, because in the 30 60 90 method the width is half of the diagonal and the only answer with 15 as the width is A
calculista

Let

x-------> the length of the rectangle

y------> the width of the rectangle

d----> the diagonal of the rectangle

we know that

The diagonal forms a pair of 30-60-90 right triangles

Step 1

Find the value of y

[tex]sin(30)=\frac{y}{d}[/tex]

Solve for y

[tex]y=sin(30)*d[/tex]

we have

[tex]sin(30)=\frac{1}{2}\\\\d=30\ in[/tex]

substitute

[tex]y=\frac{1}{2} *30=15\ in[/tex]

Step 2

Find the value of x

[tex]cos(30)=\frac{x}{d}[/tex]

Solve for x

[tex]x=cos(30)*d[/tex]

we have

[tex]cos(30)=\frac{\sqrt{3}}{2}\\\\d=30\ in[/tex]

substitute

[tex]x=\frac{\sqrt{3}}{2}*30=15\sqrt{3}\ in[/tex]

therefore

the answer is

[tex]15\ inches[/tex] by [tex]15\sqrt{3}\ inches[/tex]