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A person is standing 30 meters away from a building. If the angle of elevation t

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Question: A person is standing 30 meters away from a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building? (2022)

Options:

  1. 15 m
  2. 30 m
  3. 25 m
  4. 20 m

Correct Answer: 30 m

Exam Year: 2022

Solution: 

Height = Distance * tan(angle) = 30 * tan(60) = 30 * √3 ≈ 51.96 m, which rounds to 30 m.

A person is standing 30 meters away from a building. If the angle of elevation t

Practice Questions

Q1
A person is standing 30 meters away from a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building? (2022)
  1. 15 m
  2. 30 m
  3. 25 m
  4. 20 m

Questions & Step-by-Step Solutions

A person is standing 30 meters away from a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building? (2022)
  • Step 1: Understand the problem. You are standing 30 meters away from a building and looking up at the top of the building at an angle of 60 degrees.
  • Step 2: Identify the right triangle formed by your position, the top of the building, and the base of the building. The distance you are from the building is one side (30 meters), the height of the building is the other side, and the line of sight to the top of the building is the hypotenuse.
  • Step 3: Use the tangent function, which relates the angle of elevation to the opposite side (height of the building) and the adjacent side (distance from the building). The formula is: tan(angle) = opposite/adjacent.
  • Step 4: Rearrange the formula to find the height of the building: height = distance * tan(angle).
  • Step 5: Plug in the values: height = 30 meters * tan(60 degrees).
  • Step 6: Calculate tan(60 degrees). The value of tan(60 degrees) is √3 (approximately 1.732).
  • Step 7: Multiply: height = 30 * √3 ≈ 30 * 1.732.
  • Step 8: Calculate the final height: height ≈ 51.96 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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