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A person is standing at a distance of 20 m from a vertical pole. If the angle of

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Question: A person is standing at a distance of 20 m from a vertical pole. If the angle of elevation to the top of the pole is 45 degrees, what is the height of the pole?

Options:

  1. 20 m
  2. 10 m
  3. 30 m
  4. 15 m

Correct Answer: 20 m

Solution: 

Using tan(45°) = height/distance, we have height = distance * tan(45°) = 20 * 1 = 20 m.

A person is standing at a distance of 20 m from a vertical pole. If the angle of

Practice Questions

Q1
A person is standing at a distance of 20 m from a vertical pole. If the angle of elevation to the top of the pole is 45 degrees, what is the height of the pole?
  1. 20 m
  2. 10 m
  3. 30 m
  4. 15 m

Questions & Step-by-Step Solutions

A person is standing at a distance of 20 m from a vertical pole. If the angle of elevation to the top of the pole is 45 degrees, what is the height of the pole?
  • Step 1: Understand the problem. You have a person standing 20 meters away from a vertical pole.
  • Step 2: Know that the angle of elevation to the top of the pole is 45 degrees.
  • Step 3: Recall the tangent function in trigonometry, which relates the angle to the opposite side (height of the pole) and the adjacent side (distance from the pole).
  • Step 4: Write the formula: tan(angle) = height / distance.
  • Step 5: Substitute the known values into the formula: tan(45°) = height / 20 m.
  • Step 6: Know that tan(45°) equals 1. So, the equation becomes: 1 = height / 20 m.
  • Step 7: Solve for height by multiplying both sides by 20 m: height = 20 m * 1.
  • Step 8: Conclude that the height of the pole is 20 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 it.
  • Angle of Elevation – Understanding the concept of angle of elevation is crucial for solving problems involving heights and distances.
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