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Calculate the height of the cooling tower of a nuclear power plant if it is known that its shadow measures 271 meters in length from the base of the tower when the sun's rays fall at an angle of 30°.

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Answer to a math question Calculate the height of the cooling tower of a nuclear power plant if it is known that its shadow measures 271 meters in length from the base of the tower when the sun's rays fall at an angle of 30°.

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Clarabelle
4.7
94 Answers
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}}

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