Mathematics

Problem

Two flagstaffs stand on a horizontal plane.

A

and

B

are two points on the line joining their feet and between them. The angles of elevation of the tops of the flagstaffs as seen from

A

are

30^\circ

and

60^\circ

and as seen from

B

are

60^\circ

and

45^\circ

. If

AB

is 30 m, the distance between the flagstaffs in metres is a.

30 + 15\sqrt{3}

45 + 15\sqrt{3}

60 - 15\sqrt{3}

60 + 15\sqrt{3}