Question

# The angle of depression of $$47$$ m high building from the top of a tower $$137$$ m high is $$\displaystyle 30^{\circ}$$. Calculate the distance between the building and the tower

A
903 m
B
805 m
C
703 m
D
None of these

Solution

## The correct option is A $$\displaystyle 90\sqrt{3}$$ mLet $$AB$$ and $$CD$$ represent the tower and building respectivelyThe angle of depression $$\displaystyle \angle XAD=30^{\circ}$$In $$\displaystyle \Delta ADE,DE=CB=x$$ $$\displaystyle \angle ADE=\angle XAD=30^{\circ}(alt.\angle s)$$$$AE = AB-EB = AB - DC = (137 - 47) m = 90$$ m$$\displaystyle \therefore \tan 30^{\circ}=\frac{AE}{DE}$$$$\Rightarrow \dfrac{1}{\sqrt{3}}=\dfrac{90}{x}$$$$\Rightarrow x=90\sqrt{3}$$ mMathematics

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