The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is ?->(Show Answer!)

1. The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is

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By: anil on 05 May 2019 01.48 am

Given : CD is the tower, BD = 4 m and AD = 4 + 5 = 9 m To find : CD = $$h$$ = ? Solution : $$angle$$ DBC and $$angle$$ DAC are complementary => $$angle$$ DAC = $$ heta$$ and $$angle$$ DBC = $$(90^circ- heta)$$ In $$ riangle$$ BCD, => $$tan(90^circ- heta)=frac{CD}{DB}$$ => $$cot( heta)=frac{h}{4}$$ -----------(i) Similarly, in $$ riangle$$ ACD, => $$tan( heta)=frac{CD}{DA}$$ => $$tan( heta)=frac{h}{9}$$ -----------(ii) Multiplying equations (i) and (ii), we get : => $$tan( heta)cot( heta)=frac{h}{4} imes frac{h}{9}$$ => $$1=frac{h^2}{36}$$ => $$h^2=36$$ => $$h=sqrt{36}=6$$ m => Ans - (D)

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