Question

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

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Answer 1

x = (2√6)/3

Explanation:

Reference angle = 30°

Hypotenuse = x

Adjacent = √2

Thus, applying trigonometric ratio, we have:

Cos(30) = adj/hyp = √2/x

x*cos(30) = √2

x = √2/cos(30)

x = √2/(√3/2) (cos 30 = √3/2)

x = √2 × 2/√3

x = (2√2)/√3

Rationalize

x = (2√2 × √3)/(√3 × √3)

x = (2√6)/3