There is a 10 m tall tower between two parallel roads. The angles of depressions of the roads from the top of the tower are 30$$^\circ$$​ and 45$$^\circ$$​ respectively. Approximately how far are the roads from each other.

Correct option is B

Given:

The height of the tower = 10 m

Angle of depressions of the roads from the top of the tower = $$30^\circ$$ and $$45^\circ$$.  

Solution: 

Let the height of tower = AD 

From the road B tower distance = BD and From the road C the tower distance = DC

​$$tan45^\circ = \frac{AD}{BD} \\\ \\$$   

​$$1 = \frac{10}{BD}$$ 

BD = 10 

​$$tan30^\circ = \frac{10}{DC}$$ 

$$\frac{1}{\sqrt3} = \frac{10}{DC}$$ 

DC = $$\sqrt3\times10$$ 

Distance between the roads = BC = DC + BD =  10 +  $$\sqrt3\times10$$   = 10 + $$1.732\times10$$  = 10 + 17.32 = 27.32 m​

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