A school boy lying on the ground 30m away from the foot of a water tank tower observes that the angle of elevation of the top of the tank 60°. Calculate the height of the water tank.

  • A 60m
  • B 30 \(\sqrt{3}\)m
  • C 20 \(\sqrt{3}\)m
  • D 10 \(\sqrt{3}\)m

The correct answer is B. 30 \(\sqrt{3}\)m

We can use trigonometry to calculate the height of the water tank. The situation can be visualized as a right triangle, where the distance from the boy to the foot of the water tank tower is the base, the height of the water tank is the side opposite the angle of elevation, and the hypotenuse is the line of sight from the boy to the top of the water tank.

Given that the angle of elevation (\(\theta\)) is 60° and the distance from the boy to the foot of the tower (\(x\)) is 30m, we can use the tangent trigonometric ratio:

\(\tan(\theta) = \frac{\text{height}}{\text{base}}\)

Substitute the known values:
\(\tan(60°) = \frac{\text{height}}{30}\)
\(\sqrt{3} = \frac{\text{height}}{30}\)

Solve for the height:
\(\text{height} = 30 \cdot \sqrt{3} = 30 \sqrt{3}\)

So, the height of the water tank is \(30 \sqrt{3}\) meters.

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