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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
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B
805 m
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C
703 m
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D
None of these
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Solution

The correct option is A $$\displaystyle 90\sqrt{3}$$ m
Let $$AB$$ and $$CD$$ represent the tower and building respectively
The 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
$$\displaystyle \therefore \tan 30^{\circ}=\frac{AE}{DE}$$
$$\Rightarrow \dfrac{1}{\sqrt{3}}=\dfrac{90}{x}$$
$$\Rightarrow x=90\sqrt{3}$$ m

268970_291385_ans_c7ed2deafb5f4d3ea280438470043201.png

Mathematics

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