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?

Answer: Option A

Solution

Answer: Option A

Solution:

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