A flag staff AB $$4m$$ high is placed on a vertical tower. The angle of elevation of foot of the flag staff B at two points D,E on the ground level and lying on either side of foot of the tower are α and $$600$$ respectively with $$4m$$ and $$23$$ m as the respective distances of these points from the foot of tower. The angle subtended by the flag staff at point D is

Question

A flag staff AB $$4m$$ high is placed on a vertical tower. The angle of elevation of foot of the flag staff  B at two points D,E on the ground level and lying on either side of foot of the tower are  α and $$600$$ respectively with $$4m$$ and $$23$$  m as the respective distances of these points from the foot of tower. The angle subtended by the flag staff at point D is

Infinity Learn · Accepted Answer

From ΔBCE,$$cot$$⁡$$60$$∘$$=23x$$⇒$$x=6$$ From △ACD,$$tan$$⁡$$($$θ$$+$$α$$)=104=52$$;$$tan$$⁡α$$=32$$⇒$$tan$$⁡θ$$+321$$−$$tan$$⁡θ⋅$$32=52$$ ∵$$tan$$⁡(A+B)=$$$$tan$$⁡$$A+$$$$tan$$⁡$$B1$$−$$tan$$⁡Atan⁡B⇒$$tan$$θ$$=419$$⇒θ$$=$$$$tan$$−$$1419Therefore$$, the correct answer is $$(4).

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