The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60⁰ and the angle of elevation of the top of the second from the foot of the first tower is 30⁰. Find the top of distance between the two towers and also the height of the tower.

Given that height of one of the tower is 30 m, ∠QAB = 60° and ∠PBA = 30°

Let height of another tower be h m & distance between the towers be x m.

We need to find x and h.

So, in ∆QAB,

& in ∆PBA,

we have got the value of x, i.e. 10√3 m. So, putting the value of x in the above equation,

⇒ h = 10

Thus, we have required distance between the towers, i.e. 10√3 m

& height of another tower, i.e. 10 m.