Two flagstaffs stand on a horizontal plane

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

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 (1)

30 + 15\sqrt{3}

(2)

45 + 15\sqrt{3}

(3)

60 - 15\sqrt{3}

(4)

60 + 15\sqrt{3}