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A person is standing 40 m away from a building and sees the top of the building

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Question: A person is standing 40 m away from a building and sees the top of the building at an angle of elevation of 45 degrees. What is the height of the building? (2020)

Options:

  1. 20 m
  2. 30 m
  3. 40 m
  4. 45 m

Correct Answer: 40 m

Exam Year: 2020

Solution: 

Height = distance * tan(45) = 40 * 1 = 40 m.

A person is standing 40 m away from a building and sees the top of the building

Practice Questions

Q1
A person is standing 40 m away from a building and sees the top of the building at an angle of elevation of 45 degrees. What is the height of the building? (2020)
  1. 20 m
  2. 30 m
  3. 40 m
  4. 45 m

Questions & Step-by-Step Solutions

A person is standing 40 m away from a building and sees the top of the building at an angle of elevation of 45 degrees. What is the height of the building? (2020)
  • Step 1: Understand the problem. A person is standing 40 meters away from a building and sees the top of the building at an angle of elevation of 45 degrees.
  • Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the building, the other side is the distance from the person to the building (40 m), and the angle between the ground and the line of sight to the top of the building is 45 degrees.
  • Step 3: Recall 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 person to the building).
  • Step 4: Write the formula for tangent. tan(angle) = opposite / adjacent. Here, tan(45 degrees) = height / 40 m.
  • Step 5: Know the value of tan(45 degrees). The value of tan(45 degrees) is 1.
  • Step 6: Substitute the values into the formula. 1 = height / 40 m.
  • Step 7: Solve for the height. Multiply both sides by 40 m: height = 40 m * 1.
  • Step 8: Calculate the height. height = 40 m.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the building and the distance from the building.
  • Angle of Elevation – Understanding that the angle of elevation is measured from the horizontal line up to the line of sight to the top of the building.
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