Question

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

60°
V3
30°
X

Answer 1

4√3/3

Explanation:

Find the diagram attached below

Considering angle 60°

Opposite side = 2

Hypotenuse = x

Using the SOH CAH TOA identity

sin theta = opposite/hypotenuse

sin 60 = 2/x

x = 2/sin60

x = 2/(√3/2)

x = 2 * 2/√3

x = 4/√3

Rationalize

x = 4/√3 * √3/√3

x = 4√3/3

Hence the value of x in its simplest form is x = 4√3/3