**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:**

BD^{2} = (24 – 8)^{2} + (8 √3)^{2} = 16^{2 } + (8 √3)^{2 }

BD^{2} = 256 + 192 = 448

BD = √448 = 8√7 m

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