Answer:
x = 2 [tex]\sqrt{10}[/tex]
Step-by-step explanation:
Since the triangle is right we can use the sine ratio to find x
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{\sqrt{30} }{x}[/tex]
[ note the exact value of sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] ], hence
[tex]\frac{\sqrt{3} }{2}[/tex] = [tex]\frac{30}{x}[/tex]
multiply both sides by 2x, hence
[tex]\sqrt{3}[/tex] x = 2[tex]\sqrt{30}[/tex]
divide both sides by [tex]\sqrt{3}[/tex]
x = [tex]\frac{2\sqrt{30} }{\sqrt{3} }[/tex] = 2[tex]\sqrt{\frac{30}{3} }[/tex] = 2[tex]\sqrt{10}[/tex]
