Question

What is the value of x in simplest radical form?

Answer 1

D.
`x = (5*√(2))/(2)`

Explanation:

Reference angle = 45°

Length of Opposite side = x

Hypotenuse length = 5

Applying trigonometric ratio, we have:

`sin(45) = (x)/(5)`

Multiply both sides by 5

`5*sin(45) = (x)/(5)*5`

`5*sin(45) = x`

`5*(1)/(√(2)) = x` (sin 45 = 1/√2)

`(5)/(√(2)) = x`

Rationalize

`(5*√(2))/(√(2)*√(2)) = x`

`x = (5*√(2))/(2)`