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The top of a 15 metre high tower makes an angle of elevation of 60° with the bottom of an electric pole and angle of elevation of 30° with the top of the pole. What is the height of the electric pole ?

Correct answer: C. 10 metres

  • A. 5 metres
  • B. 8 metres
  • C. 10 metres
  • D. 12 metres

Explanation

Let the horizontal distance be d metres. From the bottom of the pole, tan 60° = 15 metres ÷ d, so d = 5√3 metres; the 30° angle from the pole's top gives a vertical difference of d tan 30° = 5 metres. Therefore, the pole height is 15 metres - 5 metres = 10 metres. Option a, 5 metres, is the vertical difference between the two tops, not the pole's full height.

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