You know all the angles in the triangle 30°, 60°, and 90°. To find the missing sides we will use:
[tex]Sin\frac{opposite}{hypotenuse} Cos\frac{adjacent}{hypotenuse} Tan\frac{opposite}{adjacent}[/tex] or [tex]S\frac{O}{H} C\frac{A}{H} T\frac{O}{A}[/tex]
sin 60° = [tex]\frac{O}{H}[/tex]
sin 60° = [tex]\frac{x}{8\sqrt{3}}[/tex]
8√3(sin 60°) = x
8√3([tex]\frac{\sqrt{3} }{2}[/tex]) = x
12 = x
cos 60° = [tex]\frac{A}{H}[/tex]
cos 60° = [tex]\frac{y}{8\sqrt{3} }[/tex]
8√3(cos 60°) = y
8√3([tex]\frac{1}{2}[/tex]) = y
4√3 = y
