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 01.56 am
BC = 2 km Let BD = x => DC = (2-x) In $$ riangle$$ABD => $$tan angle ABD = frac{AD}{BD}$$
=> $$frac{1}{sqrt{3}} = frac{AD}{x}$$ => $$x = ADsqrt{3}$$ Now, In $$ riangle$$ADC => $$tan 60 = frac{AD}{DC}$$ => $$sqrt{3} = frac{AD}{2-x}$$ => $$2sqrt{3} - 3AD = AD$$ => $$AD = frac{sqrt{3}}{2}$$
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=> $$frac{1}{sqrt{3}} = frac{AD}{x}$$ => $$x = ADsqrt{3}$$ Now, In $$ riangle$$ADC => $$tan 60 = frac{AD}{DC}$$ => $$sqrt{3} = frac{AD}{2-x}$$ => $$2sqrt{3} - 3AD = AD$$ => $$AD = frac{sqrt{3}}{2}$$