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Question

Two buildings on a plane ground are 20 m apart. From the top of the smaller building one can see the base of the taller building at an angle of depression of 50 and its top at an angle of elevation of 25. The height of the bigger building will be [Tan 50=1.2 Tan 25=0.46]


  1. 33.3 m

  2. 39.3 m

  3. 43.6 m

  4. 27.3 m


Solution

The correct option is A

33.3 m


In the given figure, let CD be the smaller building and AB be the taller building    

In Δ ADE  

Tan 50=AEDE=AE20 (as AC = DE = 20 m)  

 AE=20. Tan 50=20×1.2=24 m  

In Δ DBE  

Tan 25=BEDE=BE20 (as AC = DE = 20 m)   

 BE=20. Tan 25=20×0.46=9.3 m  

Height of the taller building =AB=AE+EB=24+9.3=33.3 m  

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