Question

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

Answer 1

Answer:

x = $\frac{8\sqrt{3} }{3}$

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin60° = $\frac{\sqrt{3} }{2}$

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{4}{x}$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

x × $\sqrt{3}$ = 8 ( divide both sides by $\sqrt{3}$ )

x = $\frac{8}{\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3} }$ ( rationalising the denominator )

x = $\frac{8\sqrt{3} }{3}$