A tower subtends angles α,$$2$$αand $$3$$α respectively at points A, B and C, all lying on a horizontal line through the foot of the tower. Then $$AB/BC=$$

Question

A tower subtends angles α,$$2$$αand $$3$$α respectively at points A, B and C, all lying on a horizontal line through the foot of the tower. Then $$AB/BC=$$

Infinity Learn · Accepted Answer

using exterior angle property ∠$$AEB=$$α and ∠$$BEC=$$ αusing sine rule                                                                                                                              From ΔABE,  ABsinα$$=BEsin$$α,FromΔBCE,BCsinα$$=BEsin3$$α⇒$$ABBC=sin3$$α$$sin$$α$$=3sin$$α−$$4sin3$$α$$sin$$α                                        $$=3$$−$$4sin2$$α$$=1+21$$−$$2sin2$$α$$=1+2cos2$$α

A tower subtends angles $α, 2 α$ and $3 α$ respectively at points A, B and C, all lying on a horizontal line through the foot of the tower. Then AB/BC=

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A tower subtends angles α,2αand 3α respectively at points A, B and C, all lying on a horizontal line through the foot of the tower. Then AB/BC=

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A tower subtends angles $α, 2 α$ and $3 α$ respectively at points A, B and C, all lying on a horizontal line through the foot of the tower. Then AB/BC=