Question

# The angle of elevation of the top of a tower from a certain point is $$\displaystyle 30^{0}$$ If the observer moves 20m towards the tower the angle of elevation of the top of the tower increases by $$\displaystyle 15^{0}$$ The height of the tower is

A
17.3m
B
21.9m
C
27.3m
D
30m

Solution

## The correct option is C $$27.3$$mLet AB be the tower and C and D be the point of observation Given  CD =20 m And $$\angle BCA=30^{0}$$ and $$\angle BDA=30+15=45^{0}$$Let height of tower is hIn triangle BAD$$tan 45^{0}=\frac{AB}{AD}\Rightarrow 1=\frac{h}{AD}\Rightarrow AD=h$$In triangle BAC$$tan 30^{0}=\frac{AB}{AC}$$ ( AC=CD+AD)$$\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{20+h}$$$$\Rightarrow \sqrt{3}h=20+h$$$$\Rightarrow \sqrt{3}h-h=20$$$$\Rightarrow h(1.732-1)=20$$$$\Rightarrow h=\frac{20}{0.732}=27.3$$Mathematics

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