1. The cliff of a mountain is 180 m high and the angles of depression of two ships on the either side of cliff are $$30^{0}$$ and $$60^{0}$$. What is the distance between the two ships ?
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By: anil on 05 May 2019 02.28 am
Given : AD is the mountain = 180 m To find : Distance between the ships = BC = ? Solution : In $$ riangle$$ ADC => $$tan(60^circ)=frac{AD}{DC}$$ => $$sqrt{3}=frac{180}{DC}$$ => $$DC=frac{180}{sqrt{3}}$$ m Similarly, in $$ riangle$$ ABD => $$tan(30^circ)=frac{AD}{BD}$$ => $$frac{1}{sqrt3}=frac{180}{BD}$$ => $$BD=180sqrt3$$ m $$ herefore$$ BC = BD + DC = $$(180sqrt3 + frac{180}{sqrt{3}})$$ = $$frac{540+180}{sqrt3}=frac{720}{sqrt3}$$ = $$240sqrt3=240 imes1.732=415.68$$ m => Ans - (C)
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