There is a tower of 10m between two parallel roads. The angles of depression of the roads from the top of the tower are 30° and 45°. How far are the roads from each other?

A. 27.32 m

B. 29.56 m

C. $$20\sqrt 3 \,{\text{m}}$$

D. $$\frac{{10}}{{\sqrt 3 }}\,{\text{m}}$$

Answer: Option A

Solution(By Examveda Team)

Angle of Depression = Angle of Elevation
Tower PS = 10 m in height
$$\eqalign{ & {\text{tan}}{45^ \circ } = 1 = \frac{{PS}}{{RS}} \cr & \therefore PS = RS = 10 \cr & \tan {30^ \circ } = \frac{1}{{\sqrt 3 }} = \frac{{PS}}{{SQ}} = \frac{{10}}{{SQ}} \cr & \therefore SQ = 10\sqrt 3 \cr & RQ = RS + SQ \cr & \,\,\,\,\,\,\,\,\,\,\, = 10 + 10\sqrt 3 \cr & \,\,\,\,\,\,\,\,\,\,\, = 27.32\,{\text{m}} \cr} $$