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A person standing 50 meters away from a building observes the top of the buildin

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Question: A person standing 50 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. 25√3 meters
  2. 50 meters
  3. 75 meters
  4. 100 meters

Correct Answer: 25√3 meters

Solution: 

Height = distance * tan(angle) = 50 * √3 = 25√3 meters.

A person standing 50 meters away from a building observes the top of the buildin

Practice Questions

Q1
A person standing 50 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. 25√3 meters
  2. 50 meters
  3. 75 meters
  4. 100 meters

Questions & Step-by-Step Solutions

A person standing 50 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?
Correct Answer: 25√3 meters
  • Step 1: Understand the situation. A person is standing 50 meters away from a building and looking up at the top of the building.
  • Step 2: Identify the angle of elevation. The angle at which the person looks up to see 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 building).
  • Step 4: Write the formula. The formula to find the height (h) of the building is: h = distance * tan(angle).
  • Step 5: Plug in the values. The distance is 50 meters and the angle is 60 degrees. So, h = 50 * tan(60 degrees).
  • Step 6: Calculate tan(60 degrees). The value of tan(60 degrees) is √3.
  • Step 7: Complete the calculation. So, h = 50 * √3.
  • Step 8: Simplify the result. The height of the building is 50√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.
  • 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 given.
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