A school boy lying on the ground 30m away from the foot of a water tank towel observes that the angle of elevation of the top of the tank is 60\(^o\). Calculate the height of the tank.

  • A 60\(\sqrt{3m}\)
  • B 30\(\sqrt{3m}\)
  • C 20\(\sqrt{3m}\)
  • D 10\(\sqrt{3m}\)
jamb 2020mathematics

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

The height of the tank can be calculated using the tangent of the angle of elevation, which is the ratio of the opposite side (the height of the tank) to the adjacent side (the distance from the boy to the tank).

In this case, the angle of elevation is 60 degrees. The tangent of 60 degrees is \(\sqrt{3}\). So, we have:

tan(60) = height / 30
\(\sqrt{3}\) = height / 30

Solving for height, we get:

height = 30 * \(\sqrt{3}\)

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