We have a triangle with angles of measures 30°, 60° and 90°. We can place the measures in the triangle as:
We can relate angles and sides with the trigonometric ratios.
We can write:
[tex]\begin{gathered} \cos (60\degree)=\frac{\text{Adyacent}}{\text{Hypotenuse}}=\frac{x}{h} \\ \sin (60\degree)=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{y}{h} \\ \tan (60\degree)=\frac{\text{Opposite}}{\text{Adyacent}}=\frac{y}{x} \end{gathered}[/tex]
From the last ratio, we can calculate x as:
[tex]\begin{gathered} \tan (60\degree)=\frac{y}{x} \\ x=\frac{y}{\tan(60\degree)}=\frac{18}{\sqrt[]{3}}=\frac{18}{\sqrt[]{3}}\cdot\frac{\sqrt[]{3}}{\sqrt[]{3}}=\frac{18\cdot\sqrt[]{3}}{3}=6\sqrt[]{3} \end{gathered}[/tex]
Answer: x = 6√3
