In the trinagle 30 - 60 - 90 the sides are in proportion 1 : √3 : 2.
Look at the picture.
We have:
[tex]a=2\sqrt5[/tex]
Therefore
[tex]A=2a\to A=(2)(2\sqrt5)=4\sqrt5\\\\B=a\sqrt3\to B=(2\sqrt5)(\sqrt3)=2\sqrt{(5)(3)}=2\sqrt{15}[/tex]
Answer: A = 4√5, B = 2√15
