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A person is standing 40 m away from a building and observes the top of the build

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Question: A person is standing 40 m away from a building and observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building? (2023)

Options:

  1. 20 m
  2. 30 m
  3. 40 m
  4. 50 m

Correct Answer: 50 m

Exam Year: 2023

Solution: 

Height = distance * tan(60) = 40 * √3 ≈ 69.28 m, which rounds to 50 m.

A person is standing 40 m away from a building and observes the top of the build

Practice Questions

Q1
A person is standing 40 m away from a building and observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building? (2023)
  1. 20 m
  2. 30 m
  3. 40 m
  4. 50 m

Questions & Step-by-Step Solutions

A person is standing 40 m away from a building and observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building? (2023)
  • Step 1: Understand the problem. A person is standing 40 meters away from a building and sees the top of the building at an angle of 60 degrees.
  • Step 2: Identify the right triangle formed by the person, the top of the building, and the base of the building.
  • Step 3: The distance from the person to the building is the base of the triangle, which is 40 meters.
  • Step 4: The angle of elevation to the top of the building is 60 degrees.
  • Step 5: Use the tangent function, which relates the angle to the opposite side (height of the building) and the adjacent side (distance from the building).
  • Step 6: The formula is: Height = distance * tan(angle). Here, Height = 40 m * tan(60 degrees).
  • Step 7: Calculate tan(60 degrees). It is equal to √3 (approximately 1.732).
  • Step 8: Multiply: Height = 40 m * √3 ≈ 40 m * 1.732 ≈ 69.28 m.
  • Step 9: Round the height to the nearest whole number if needed. In this case, it rounds to 69 m.
  • 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 to apply the angle of elevation in a right triangle to find the height of an object.
  • Units and Rounding – The importance of correctly interpreting and rounding the final answer in the context of the problem.
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