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A person is standing 25 meters away from a building and sees the top of the buil

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Question: A person is standing 25 meters away from a building and sees the top of the building at an angle of elevation of 30 degrees. What is the height of the building?

Options:

  1. 25/√3 meters
  2. 15 meters
  3. 20 meters
  4. 10 meters

Correct Answer: 25/√3 meters

Solution: 

Using tan(30) = height/25, height = 25 * (1/√3) = 25/√3 meters.

A person is standing 25 meters away from a building and sees the top of the buil

Practice Questions

Q1
A person is standing 25 meters away from a building and sees the top of the building at an angle of elevation of 30 degrees. What is the height of the building?
  1. 25/√3 meters
  2. 15 meters
  3. 20 meters
  4. 10 meters

Questions & Step-by-Step Solutions

A person is standing 25 meters away from a building and sees the top of the building at an angle of elevation of 30 degrees. What is the height of the building?
  • Step 1: Understand the situation. A person is standing 25 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 30 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 equation using the tangent function: tan(30 degrees) = height / 25 meters.
  • Step 5: Find the value of tan(30 degrees). It is equal to 1/√3.
  • Step 6: Substitute the value of tan(30 degrees) into the equation: 1/√3 = height / 25.
  • Step 7: Rearrange the equation to solve for height: height = 25 * (1/√3).
  • Step 8: Calculate the height: height = 25/√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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