Q. 34

The angles of dep

Answer :


Let AB and CD be the multi-storeyed building and the building respectively. Let the height of the multi-storeyed building = h m and the distance between the two buildings = x m.


AE = CD = 8 m [Given]


BE = AB – AE = (h – 8) m


and AC = DE = x m [Given]


Also, FBD = BDE = 30° (Alternate angles)


FBC = BCA = 45° (Alternate angles) 1/2


Now,


In Δ ACB, In Δ BDE,


tan 45° =



x = h ….. (i) 1


In ΔBDE,


tan30° =



….. (ii)


From (i) and (ii), we get,


h = √3 – 8√3


√3h – h =8√3


h (√3 – 1) = 8√3


h =


h =


h – = 4√3 (√3 + 1)


h = 12 + 4√3 m


Distance between the two building


OR



From the figure, the angle of elevation for the first position of the balloon


EAD = 60° and for second position BAC = 30°.


The vertical distance 1


ED = CB = 88.2 – 1.2 = 87 m.


Let AD = x m and AB = y m.


Then in right Δ ADE, tan 60° =



…….(i) 1


In right ΔABC, tan 30° =



y = 87√3 ..….(ii)


Subtracting (i) and (ii) 1


y – x = 87√3 –


y – x = 1


y – x = 58√3 m


Hence, the distance travelled by the balloon is equal to BD


y – x = 58√3 m.


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