There is a 10 m tall tower between two parallel roads. The angles of depression of the roads from the top of the tower are 30° and 45° respectively. Approximately, how far are the roads from each other?
27.32 m
The correct answer is Option 3 i.e. 27.32 m.
In △ABD
⇒ tan 45° = AD/BD
⇒ 1 = 10/BD
⇒ BD = 10
In △ACD
⇒ tan 30° = 10/DC
⇒ \(1\over \sqrt3\) = \(10 \over DC\)
⇒ DC = \(\sqrt3\) × 10
Distance between the roads = BC = BD + DC
⇒ 10 + \(\sqrt3\) × 10
⇒ 10 + 1.732 × 10
⇒ 10 + 17.32 = 27.32 m
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