Question

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

Answer 1

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

Answer 2

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

`sin(30)=(y)/(d)`

Solve for y

`y=sin(30)*d`

we have

`sin(30)=(1)/(2)\\\\d=30\ in`

substitute

`y=(1)/(2) *30=15\ in`

Step 2

Find the value of x

`cos(30)=(x)/(d)`

Solve for x

`x=cos(30)*d`

we have

`cos(30)=(√(3))/(2)\\\\d=30\ in`

substitute

`x=(√(3))/(2)*30=15√(3)\ in`

therefore

the answer is

`15\ inches` by
`15√(3)\ inches`