Solution:

Consider the height of the first tower TR = x

It is given that

Height of the second tower PQ = 60 m

Distance between the two towers QR = 140 m

Construct PL parallel to QR

LR = PQ = 60 m

PL = QR = 140 m

So we get

TL = (x – 60) m

In right triangle TPL

tan θ = TL/PL

Substituting the values

tan 30⁰ = (x – 60)/ 140

So we get

1/√3 = (x – 60)/ 140

By further calculation

x – 60 = 140/√3

Multiply and divide by √3

x – 60 = 140/√3 × √3/√3 = 140√3/3

We get

x = 140√3/3 + 60

x = (140 × 1.732)/ 3 + 60

x = 80.83 + 60

x = 140.83

Hence, the height of first tower is 140.83 m.