Question

q. on the same side of a tower two objects are located. observed from the top of the tower their angles of depression are 45?? and 60??. if the height of the tower is 600 m the distance between the objects is approximately equal to :

Answer 1

Let DC be the tower and A and B be the objects as shown above.
Given that DC = 600 m , DAC = 45°, DBC = 60°

tan 60°=DCBC√3=600BCBC= 600√3⋯(1)tan 60°=DCBC3=600BCBC= 6003⋯(1)

tan 45°=DCAC1=600ACAC= 600⋯(2)tan 45°=DCAC1=600ACAC= 600⋯(2)

Distance between the objects 
= AB = (AC - BC)
=600−600√3=600−6003 [∵ from (1) and (2)]
=600(1−1√3)=600(√3−1√3)=600(√3−1√3)×√3√3=600√3(√3−1)3=200√3(√3−1)=200(3−√3)=200(3−1.73)=254 m=600(1−13)=600(3−13)=600(3−13)×33=6003(3−1)3=2003(3−1)=200(3−3)=200(3−1.73)=254 m