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A person is standing 40 meters away from a building and sees the top of the buil

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Question: A person is standing 40 meters away from a building and sees the top of the building at an angle of elevation of 60 degrees. What is the height of the building?

Options:

  1. 20√3 meters
  2. 40 meters
  3. 30 meters
  4. 50 meters

Correct Answer: 20√3 meters

Solution: 

Using tan(60°) = height / 40, height = 40 * tan(60°) = 40 * √3 ≈ 69.28 meters.

A person is standing 40 meters away from a building and sees the top of the buil

Practice Questions

Q1
A person is standing 40 meters away from a building and sees the top of the building at an angle of elevation of 60 degrees. What is the height of the building?
  1. 20√3 meters
  2. 40 meters
  3. 30 meters
  4. 50 meters

Questions & Step-by-Step Solutions

A person is standing 40 meters away from a building and sees the top of the building at an angle of elevation of 60 degrees. What is the height of the building?
  • 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 elevation of 60 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 the person to the building (40 meters), and the angle between the ground and the line of sight to the top of the building is 60 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 person to the building). So, tan(60°) = height / 40.
  • Step 4: Rearrange the equation to find the height. Multiply both sides by 40: height = 40 * tan(60°).
  • Step 5: Calculate tan(60°). The value of tan(60°) is √3 (approximately 1.732).
  • Step 6: Substitute the value of tan(60°) into the equation: height = 40 * √3.
  • Step 7: Calculate the height: height ≈ 40 * 1.732 ≈ 69.28 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.
  • Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the building, the distance from the building, and the line of sight.
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