Let's denote the height of the cooling tower as h meters.
Given that the length of the shadow is 271 meters and the angle of elevation is 30°, we can set up the following trigonometric equation:
\tan(30^\circ) = \dfrac{h}{271}
Solving for h :
h = 271 \cdot \tan(30^\circ)
h = 271 \cdot \dfrac{\sqrt{3}}{3}
h = 271 \cdot \dfrac{1.732}{3}
h = 271 \cdot 0.577
h \approx 156.367 \, \text{meters}
Therefore, the height of the cooling tower is approximately 156.367 meters.
\boxed{h \approx 156.367 \text{ meters}}