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A person is 12 meters away from a building. If the angle of elevation to the top

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Question: A person is 12 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?

Options:

  1. 6 meters
  2. 12 meters
  3. 18 meters
  4. 24 meters

Correct Answer: 6 meters

Solution: 

Height = distance * tan(30) = 12 * (1/√3) = 12/√3 = 4√3 meters ≈ 6 meters.

A person is 12 meters away from a building. If the angle of elevation to the top

Practice Questions

Q1
A person is 12 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?
  1. 6 meters
  2. 12 meters
  3. 18 meters
  4. 24 meters

Questions & Step-by-Step Solutions

A person is 12 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?
  • Step 1: Understand the problem. You have a person standing 12 meters away from a building and looking up at the top of the building at an angle of 30 degrees.
  • Step 2: Identify the right triangle formed by the person, the top of the building, and the base of the building. The distance from the person to the building is one side (12 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: Plug in the values. For an angle of 30 degrees, tan(30) = 1/√3. The formula becomes: tan(30) = height / 12.
  • Step 5: Rearrange the formula to find the height: height = 12 * tan(30).
  • Step 6: Substitute tan(30) with 1/√3: height = 12 * (1/√3).
  • Step 7: Calculate the height: height = 12/√3.
  • Step 8: To simplify, multiply the numerator and denominator by √3: height = (12√3)/3 = 4√3 meters.
  • Step 9: If needed, approximate the height: 4√3 is approximately 6 meters.
  • Trigonometry – The problem tests the understanding of basic trigonometric functions, specifically the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle.
  • Angle of Elevation – The question involves calculating the height of an object (the building) based on the angle of elevation from a certain distance.
  • Right Triangle Properties – The problem requires knowledge of right triangle properties and how to apply them to find unknown lengths using trigonometric ratios.
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