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

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Question: A person is 40 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. 20√3 meters
  2. 30 meters
  3. 40 meters
  4. 10√3 meters

Correct Answer: 20√3 meters

Solution: 

Using tan(30°) = height / distance, we have height = distance * tan(30°) = 40 * (1/√3) = 40/√3 = 20√3 meters.

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

Practice Questions

Q1
A person is 40 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. 20√3 meters
  2. 30 meters
  3. 40 meters
  4. 10√3 meters

Questions & Step-by-Step Solutions

A person is 40 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 problem. You are 40 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 your position, the top of the building, and the base of the building. The distance from you to the building is one side (40 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: Substitute the known values into the formula. Here, angle = 30 degrees, opposite = height, and adjacent = 40 meters. So, tan(30°) = height / 40.
  • Step 5: Solve for height. Rearranging the formula gives height = 40 * tan(30°).
  • Step 6: Calculate tan(30°). The value of tan(30°) is 1/√3.
  • Step 7: Substitute tan(30°) back into the equation: height = 40 * (1/√3).
  • Step 8: Simplify the equation: height = 40/√3.
  • Step 9: To make it easier to understand, multiply the numerator and denominator by √3: height = (40√3)/3.
  • Step 10: The final height of the building is approximately 20√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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