1. If the angles of elevation of a balloon from two consecutive kilometre-stones along a road are 30° and 60° respectively, then the height of the balloon above the
ground will be
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By: anil on 05 May 2019 01.58 am
It is given that BC = 2 km Let BD = x => CD = (2 - x) km From $$ riangle$$ABD => $$tan 30 = frac{AD}{BD}$$ => $$frac{1}{sqrt{3}} = frac{AD}{x}$$ => $$AD = frac{x}{sqrt{3}}$$ From $$ riangle$$ADC => $$tan 60 = frac{AD}{CD}$$ => $$sqrt{3} = frac{frac{x}{sqrt{3}}}{2 - x}$$ => $$3 (2 - x) = x$$ => $$x = frac{3}{2}$$ Now, height of balloon above ground = $$AD = frac{frac{3}{2}}{sqrt{3}}$$ = $$frac{sqrt{3}}{2}$$ km
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It is given that BC = 2 km Let BD = x => CD = (2 - x) km From $$ riangle$$ABD => $$tan 30 = frac{AD}{BD}$$ => $$frac{1}{sqrt{3}} = frac{AD}{x}$$ => $$AD = frac{x}{sqrt{3}}$$ From $$ riangle$$ADC => $$tan 60 = frac{AD}{CD}$$ => $$sqrt{3} = frac{frac{x}{sqrt{3}}}{2 - x}$$ => $$3 (2 - x) = x$$ => $$x = frac{3}{2}$$ Now, height of balloon above ground = $$AD = frac{frac{3}{2}}{sqrt{3}}$$ = $$frac{sqrt{3}}{2}$$ km