Question

Angle of depression of the top and bottom of 8 metre high tower building from the top of a motorized bill

Answer 1

Let CD be the multi-storey building. Hence we also get that LDBC = 45. Since tan45 = 1, DC = CB. 
Now let the height of the multi-storey building be 'x'. Extend BA to meet the above horizontal line at E. EA = x - 8. Since tan30= 1/√3, implies ED= √3 x ( x -      8 ).
Since, ED = CB = DC;
Hence, √3 x ( x - 8 ) = x.
Solving this equation we get, x = 8√3 / √3 - 1
Simplifying which we get x = 12 + 4√3, which is equal to both height of the building and the distance between the two buildings! :-)
Hope its helpful!
Do check the calculations though ..

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