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A person standing 25 meters away from a building observes the top of the buildin

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Question: A person standing 25 meters away from a building observes the top of the building at an angle of elevation of 53 degrees. What is the height of the building?

Options:

  1. 15 meters
  2. 20 meters
  3. 30 meters
  4. 40 meters

Correct Answer: 30 meters

Solution: 

Height = distance * tan(angle) = 25 * tan(53) ≈ 25 * 1.327 = 33.175 meters.

A person standing 25 meters away from a building observes the top of the buildin

Practice Questions

Q1
A person standing 25 meters away from a building observes the top of the building at an angle of elevation of 53 degrees. What is the height of the building?
  1. 15 meters
  2. 20 meters
  3. 30 meters
  4. 40 meters

Questions & Step-by-Step Solutions

A person standing 25 meters away from a building observes the top of the building at an angle of elevation of 53 degrees. What is the height of the building?
Correct Answer: 33.175 meters
  • Step 1: Understand the problem. You are standing 25 meters away from a building and looking up at the top of the building at an angle of 53 degrees.
  • Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the building, the other side is the distance from you to the building (25 meters), and the angle between the ground and your line of sight to the top of the building is 53 degrees.
  • Step 3: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the building) divided by the adjacent side (distance from the building). So, tan(angle) = height / distance.
  • Step 4: Rearrange the formula to find the height. Height = distance * tan(angle).
  • Step 5: Plug in the values. Height = 25 meters * tan(53 degrees).
  • Step 6: Calculate tan(53 degrees). Using a calculator, tan(53 degrees) is approximately 1.327.
  • Step 7: Multiply the distance by the tangent value. Height = 25 * 1.327.
  • Step 8: Perform the multiplication. Height ≈ 33.175 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 the observer.
  • Angle of Elevation – Understanding how the angle of elevation is measured from the horizontal line to the line of sight to the top of the building.
  • 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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