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A person is standing 10 meters away from a vertical pole. If the angle of elevat

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Question: A person is standing 10 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?

Options:

  1. 5√3 meters
  2. 10 meters
  3. 15 meters
  4. 20 meters

Correct Answer: 5√3 meters

Solution: 

Height = distance * tan(60) = 10 * √3 = 10√3 meters.

A person is standing 10 meters away from a vertical pole. If the angle of elevat

Practice Questions

Q1
A person is standing 10 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?
  1. 5√3 meters
  2. 10 meters
  3. 15 meters
  4. 20 meters

Questions & Step-by-Step Solutions

A person is standing 10 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?
  • Step 1: Understand the scenario. A person is standing 10 meters away from a vertical pole.
  • Step 2: Identify the angle of elevation to the top of the pole, which is 60 degrees.
  • Step 3: Visualize a right triangle formed by the pole, the ground, and the line of sight to the top of the pole.
  • Step 4: In this triangle, the distance from the person to the pole is the base (10 meters), and the height of the pole is the opposite side.
  • Step 5: Use the tangent function, which relates the angle to the opposite side and the adjacent side: tan(angle) = opposite/adjacent.
  • Step 6: For our problem, tan(60 degrees) = height / 10 meters.
  • Step 7: Rearrange the formula to find the height: height = 10 * tan(60 degrees).
  • Step 8: Calculate tan(60 degrees), which is √3.
  • Step 9: Substitute tan(60 degrees) into the equation: height = 10 * √3.
  • Step 10: The height of the pole is 10√3 meters.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the pole and the distance from the pole.
  • Angle of Elevation – Understanding how the angle of elevation from a point to the top of an object can be used to calculate the height of that object.
  • Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the pole is the opposite side, the distance from the pole is the adjacent side, and the angle of elevation is the angle between them.
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