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A person is standing on the ground and looking at the top of a building. If the

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Question: A person is standing on the ground and looking at the top of a building. If the angle of elevation is 45 degrees and the person is 20 meters away from the building, what is the height of the building?

Options:

  1. 20 meters
  2. 10 meters
  3. 30 meters
  4. 25 meters

Correct Answer: 20 meters

Solution: 

Height = distance * tan(angle) = 20 * 1 = 20 meters.

A person is standing on the ground and looking at the top of a building. If the

Practice Questions

Q1
A person is standing on the ground and looking at the top of a building. If the angle of elevation is 45 degrees and the person is 20 meters away from the building, what is the height of the building?
  1. 20 meters
  2. 10 meters
  3. 30 meters
  4. 25 meters

Questions & Step-by-Step Solutions

A person is standing on the ground and looking at the top of a building. If the angle of elevation is 45 degrees and the person is 20 meters away from the building, what is the height of the building?
  • Step 1: Understand the scenario. A person is looking at the top of a building from a distance of 20 meters away.
  • Step 2: Identify the angle of elevation. The angle at which the person looks up to the top of the building is 45 degrees.
  • Step 3: Recall the relationship between the angle of elevation, height of the building, and distance from the building. We can use the tangent function: tan(angle) = height / distance.
  • Step 4: Since the angle is 45 degrees, we know that tan(45 degrees) = 1.
  • Step 5: Use the formula: height = distance * tan(angle). Here, distance is 20 meters and tan(45 degrees) is 1.
  • Step 6: Calculate the height: height = 20 * 1 = 20 meters.
  • Step 7: Conclude that the height of the building is 20 meters.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the building 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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