Question

Find the length of side x in simplest radical form with a rational denominator

Answer 1

(4
`√(3)`)/3

Explanation:

From the diagram,

Applying

sinθ = Opposite/Hypotenuse................. Equation 1

From the diagram,

Given: θ = 60°, Opposite = 2, Hypotenuse = X

Substitute these values into equation 1

sin60° = 2/X

make X the subject of the equation

X = 2/sin60°.................. Equation 2

But,

sin60° =
`(√(3) )/(2)`

Therefore,

X = 2/(
`(√(3) )/(2)`)

X = (2×2)/
`√(3)`

X = 4/
`√(3)`

Rationalising the denominator,

X = (4/
`√(3)`)×(
`√(3)`/
`√(3)`)

X = (4
`√(3)`)/3