Q) The angle of elevation of the top of a tower 24 m high from the foot of another tower in the same plane is 60°. The angle of elevation of the top of second tower from the foot of the first tower is 30°. Find the distance between two towers and the height of the other tower. Also, find the length of the wire attached to the tops of both the towers.

Ans: 

Let AB and CD be the towers where AB is first tower of 24m height

Let Height of the other tower be h and distance between both of the towers be d

Therefore, in Δ BAC, tan 60°  = 

       √3 =    or d =  8√3 m

Also, in Δ DAC, tan 30° = 

        h =   or h = 8 m

Calculation for Length of the wire BD in Δ BDE:

BD² = (24 – 8)² + (8 √3)² = 16²  + (8 √3)² 

BD² =  256 + 192 = 448

BD = √448  = 8√7 m

Therefore, the length of wire between tops of two towers is 8√7 m