We have a right triangle we angles 30°, 60° and 90°.
We can draw the triangle for better:
We know that CB=20 cm, so:
[tex]\begin{gathered} \cos 60=\frac{1}{2}=\frac{AC}{CB}=\frac{AC}{20} \\ AC=\frac{20}{2}=10 \\ \text{And for pythagoras theorem:} \\ AB^2+AC^2=CB^2 \\ AB^2+10^2=20^2 \\ AB=\sqrt[]{400-100}=\sqrt[]{300}=17.32 \\ AB=\sqrt[]{3\cdot100}=10\sqrt[]{3} \end{gathered}[/tex]
So, the short leg is 10 cm and long leg is 17.32 cm.
