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A person standing 40 meters away from a building observes the top of the buildin

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

Options:

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

Correct Answer: 40√3 meters

Solution: 

Height = distance * tan(angle) = 40 * tan(60°) = 40√3 meters.

A person standing 40 meters away from a building observes the top of the buildin

Practice Questions

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

Questions & Step-by-Step Solutions

A person standing 40 meters away from a building observes 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. You have a person standing 40 meters away from a building and looking up at the top of the building at an angle 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 of elevation is 60 degrees.
  • Step 3: Recall 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).
  • Step 4: Write the formula for height. The height of the building can be calculated using the formula: Height = distance * tan(angle).
  • Step 5: Plug in the values. Here, the distance is 40 meters and the angle is 60 degrees. So, Height = 40 * tan(60°).
  • Step 6: Calculate tan(60°). The value of tan(60°) is √3.
  • Step 7: Complete the calculation. Height = 40 * √3 meters.
  • Step 8: Final answer. The height of the building is 40√3 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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