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]
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