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A person is standing 25 meters away from a vertical pole. If the angle of elevat

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Question: A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 53 degrees, what is the height of the pole?

Options:

  1. 15 meters
  2. 20 meters
  3. 25 meters
  4. 30 meters

Correct Answer: 20 meters

Solution: 

Height = distance * tan(angle) = 25 * tan(53°) ≈ 25 * 1.327 = 20.68 meters.

A person is standing 25 meters away from a vertical pole. If the angle of elevat

Practice Questions

Q1
A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 53 degrees, what is the height of the pole?
  1. 15 meters
  2. 20 meters
  3. 25 meters
  4. 30 meters

Questions & Step-by-Step Solutions

A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 53 degrees, what is the height of the pole?
Correct Answer: 20.68 meters
  • Step 1: Understand the problem. You have a person standing 25 meters away from a vertical pole and looking up at the top of the pole.
  • Step 2: Identify the angle of elevation. The angle at which the person looks up to the top of the pole is 53 degrees.
  • Step 3: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the pole) divided by the adjacent side (distance from the pole).
  • Step 4: Set up the equation. The height of the pole can be found using the formula: Height = distance * tan(angle).
  • Step 5: Plug in the values. Here, the distance is 25 meters and the angle is 53 degrees. So, Height = 25 * tan(53°).
  • Step 6: Calculate tan(53°). Using a calculator, tan(53°) is approximately 1.327.
  • Step 7: Multiply the distance by the tangent value. So, Height = 25 * 1.327.
  • Step 8: Perform the multiplication. 25 * 1.327 = 20.68 meters.
  • Step 9: Conclusion. The height of the pole is approximately 20.68 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 the concept of angle of elevation is crucial for solving problems involving heights and distances.
  • 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 formed.
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