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A man is standing on the deck of a ship. which is 10 m above water level. Heobserves the angle of elevation of the topof a hill as 45" and the angle of depressionof the base of the hill as 30". Calculate thedistance of the hill from the ship and theheight of the hill(A) 17.32 m. 27.3 m(B) 18.32 m. 28.3 m(C) 17.89 m. 28.3 m(D) 8.32 m. 29.2 m |
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Answer» Let a man is standing on the Deck of a ship at point a such that AB = 10 m & let CE be the hillThus, AB = CD = 10 mThe top and bottom of a hill is E and C.Given, the angle of depression of the base C of the hill observed from A is 30° and angle of elevation of the top of the hill observed from A is 60 °Then ∠EAD= 60° &∠CAE= ∠BCA= 30°. (Alternate ANGLES)Let AD = BC = x m & DE= h MIN ∆ ADEtan 60° = Perpendicular / base = DE/AD√3= h/x [TAN 60° = √3]h = √3x……..(1)In ∆ ABCtan 30° = AB /BC[ tan30° = 1/√3]1/√3 = 10/xx= 10√3 m.. …………..(2)Substitute the value of x from EQUATION (2) in equation (1), we have h = √3xh= √3× 10√3= 10 × 3= 30 mh = 30 mThe height of the hill is CE= CD+ DE= 10 +30= 40 mHence, the height of the hill is 40 m & the Distance of the hill from the ship is 10√3 m. |
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