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A person standing 50 meters away from a building observes the top of the buildin

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Question: A person standing 50 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. 25 meters
  2. 50 meters
  3. 35 meters
  4. 45 meters

Correct Answer: 50 meters

Solution: 

Height = distance * tan(angle) = 50 * tan(45°) = 50 meters.

A person standing 50 meters away from a building observes the top of the buildin

Practice Questions

Q1
A person standing 50 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. 25 meters
  2. 50 meters
  3. 35 meters
  4. 45 meters

Questions & Step-by-Step Solutions

A person standing 50 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 50 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 the relationship between the height of the building, the distance from the building, and the angle of elevation. We can use the tangent function.
  • Step 4: The formula to find the height (h) of the building is: height = distance * tan(angle).
  • Step 5: Plug in the values: distance = 50 meters and angle = 45 degrees.
  • Step 6: Calculate tan(45 degrees). The value of tan(45 degrees) is 1.
  • Step 7: Now, substitute the values into the formula: height = 50 * tan(45 degrees) = 50 * 1.
  • Step 8: Calculate the height: height = 50 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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