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A person looks at the top of a building from a distance of 50 meters. If the ang

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Question: A person looks at the top of a building from a distance of 50 meters. If the angle of elevation is 30 degrees, what is the height of the building?

Options:

  1. 25 meters
  2. 30 meters
  3. 35 meters
  4. 40 meters

Correct Answer: 25 meters

Solution: 

Height = distance * tan(30) = 50 * (1/√3) ≈ 25 meters.

A person looks at the top of a building from a distance of 50 meters. If the ang

Practice Questions

Q1
A person looks at the top of a building from a distance of 50 meters. If the angle of elevation is 30 degrees, what is the height of the building?
  1. 25 meters
  2. 30 meters
  3. 35 meters
  4. 40 meters

Questions & Step-by-Step Solutions

A person looks at the top of a building from a distance of 50 meters. If the angle of elevation is 30 degrees, what is the height of the building?
Correct Answer: 25 meters
  • Step 1: Understand the problem. You are looking at the top of a building from a distance of 50 meters away.
  • Step 2: Identify the angle of elevation. The angle of elevation to the top of the building is 30 degrees.
  • Step 3: Recall the relationship in a right triangle. The height of the building (opposite side) and the distance from the building (adjacent side) can be related using the tangent function.
  • Step 4: Write the formula for tangent. The formula is: tan(angle) = opposite/adjacent.
  • Step 5: Substitute the known values into the formula. Here, opposite is the height of the building (H), and adjacent is the distance (50 meters). So, tan(30 degrees) = H / 50.
  • Step 6: Solve for the height (H). Rearranging gives H = 50 * tan(30 degrees).
  • Step 7: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3.
  • Step 8: Substitute this value back into the equation. H = 50 * (1/√3).
  • Step 9: Calculate the height. H ≈ 50 * 0.577 ≈ 25 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 is the adjacent side, and the angle of elevation is given.
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