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

The length of side X in the simplest radical form is 10/√3

The triangle is right angled, therefore we can apply trigonometry :

To obtain the value of X which is the hypotenus :

Using SOHCAHTOA:

Cosθ = adjacent / hypotenus

Cos 30 = 5 / X

√3/2 = 5 / X

√3 / 2 × X = 5

X = 5 ÷ √3 / 2

X = 5 × 2 / √3

X = 10/√3

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