Question

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

Answer 1

Answer:

(4$\sqrt{3}$)/3

Step-by-step 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° = $\frac{\sqrt{3} }{2}$

Therefore,

X = 2/( $\frac{\sqrt{3} }{2}$)

X = (2×2)/$\sqrt{3}$

X = 4/$\sqrt{3}$

Rationalising the denominator,

X = (4/$\sqrt{3}$)×($\sqrt{3}$/$\sqrt{3}$)

X = (4$\sqrt{3}$)/3