Question 40
Three people $A,B,C$ stand near the junction of two perpendicular roads. $A$ is exactly at the junction, while $B,C$ are on different roads. In the nearby field, inside the right angle $CAB$, a billboard is supported by posts at $D,E$, exactly one metre apart. All three people see the front of the billboard. If $\angle DAE,\angle DBE,\angle DCE$ are all $30^\circ$, what is the straight-line distance from $B$ to $C$?
(A) $3/2\,\mathrm m$ (B) $(1+\sqrt5)/2\,\mathrm m$ (C) $\sqrt3\,\mathrm m$
(D) $2\,\mathrm m$ (E) It cannot be determined.
(A) $3/2\,\mathrm m$ (B) $(1+\sqrt5)/2\,\mathrm m$ (C) $\sqrt3\,\mathrm m$
(D) $2\,\mathrm m$ (E) It cannot be determined.