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A person standing 15 meters away from a building observes the top of the buildin

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Question: A person standing 15 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. 10 m
  2. 15 m
  3. 20 m
  4. 30 m

Correct Answer: 15 m

Solution: 

Height = distance * tan(45) = 15 * 1 = 15 m

A person standing 15 meters away from a building observes the top of the buildin

Practice Questions

Q1
A person standing 15 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. 10 m
  2. 15 m
  3. 20 m
  4. 30 m

Questions & Step-by-Step Solutions

A person standing 15 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?
  • Step 1: Understand the situation. A person is standing 15 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 15 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 = 15 meters * 1.
  • Step 8: Calculate the height: height = 15 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 given.
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