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

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Question: A man is standing on the ground and looking at the top of a building. If the angle of elevation is 45 degrees and he is 10 meters away from the building, what is the height of the building?

Options:

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

Correct Answer: 10 meters

Solution: 

Height = distance * tan(angle) = 10 * tan(45°) = 10 meters.

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

Practice Questions

Q1
A man is standing on the ground and looking at the top of a building. If the angle of elevation is 45 degrees and he is 10 meters away from the building, what is the height of the building?
  1. 10 meters
  2. 5 meters
  3. 15 meters
  4. 20 meters

Questions & Step-by-Step Solutions

A man is standing on the ground and looking at the top of a building. If the angle of elevation is 45 degrees and he is 10 meters away from the building, what is the height of the building?
  • Step 1: Understand the problem. A man is looking at the top of a building from a distance of 10 meters away.
  • Step 2: Identify the angle of elevation. The angle at which he is looking up to the top of the building is 45 degrees.
  • Step 3: Recall the formula to find the height of the building. The height can be calculated using the formula: Height = distance * tan(angle).
  • Step 4: Plug in the values into the formula. Here, the distance is 10 meters and the angle is 45 degrees.
  • Step 5: Calculate tan(45 degrees). The value of tan(45 degrees) is 1.
  • Step 6: Multiply the distance by the value of tan(45 degrees). So, Height = 10 * 1.
  • Step 7: Find the height of the building. Therefore, the height of the building is 10 meters.
  • Trigonometry – The problem tests the understanding of the tangent function in right triangles, specifically how to calculate height using the angle of elevation.
  • Angle of Elevation – Understanding the concept of angle of elevation and its application in real-world scenarios.
  • Distance Measurement – The importance of accurately interpreting the distance from the observer to the object being measured.
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