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A person standing 20 meters away from a building observes the top of the buildin

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Question: A person standing 20 meters away from a building observes the top of the building at an angle of elevation of 45 degrees. What is the height of the building?

Options:

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

Correct Answer: 20 meters

Solution: 

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

A person standing 20 meters away from a building observes the top of the buildin

Practice Questions

Q1
A person standing 20 meters away from a building observes the top of the building at an angle of elevation of 45 degrees. What is the height of the building?
  1. 20 meters
  2. 10 meters
  3. 30 meters
  4. 15 meters

Questions & Step-by-Step Solutions

A person standing 20 meters away from a building observes the top of the building at an angle of elevation of 45 degrees. What is the height of the building?
Correct Answer: 20 meters
  • Step 1: Understand the situation. A person is standing 20 meters away from a building.
  • Step 2: The person looks up at the top of the building and sees it at an angle of elevation of 45 degrees.
  • Step 3: Recall that the angle of elevation is the angle between the horizontal line (the ground) and the line of sight to the top of the building.
  • Step 4: Use the tangent function from trigonometry. The formula is: height = distance * tan(angle).
  • Step 5: Plug in the values. The distance is 20 meters and the angle is 45 degrees.
  • Step 6: Calculate tan(45 degrees). The value of tan(45 degrees) is 1.
  • Step 7: Multiply the distance by the tangent value: height = 20 meters * 1.
  • Step 8: The result is 20 meters. Therefore, 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 how the angle of elevation from a point to the top of an object can be used to calculate height.
  • Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the building is the opposite side, the distance from the building is the adjacent side, and the angle of elevation is the angle between them.
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