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A person is standing 40 meters away from a building. If the angle of elevation t

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Question: A person is standing 40 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?

Options:

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

Correct Answer: 40 meters

Solution: 

Height = distance * tan(angle) = 40 * 1 = 40 meters.

A person is standing 40 meters away from a building. If the angle of elevation t

Practice Questions

Q1
A person is standing 40 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?
  1. 20 meters
  2. 30 meters
  3. 40 meters
  4. 45 meters

Questions & Step-by-Step Solutions

A person is standing 40 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?
Correct Answer: 40 meters
  • Step 1: Understand the problem. You have a person standing 40 meters away from a building.
  • Step 2: Know that the angle of elevation to the top of the building is 45 degrees.
  • Step 3: Remember that the tangent of an angle in a right triangle is the opposite side (height of the building) divided by the adjacent side (distance from the building).
  • Step 4: Use the formula: Height = distance * tan(angle).
  • Step 5: Substitute the values into the formula: Height = 40 meters * tan(45 degrees).
  • Step 6: Know that tan(45 degrees) equals 1.
  • Step 7: Calculate the height: Height = 40 meters * 1 = 40 meters.
  • Step 8: Conclude that the height of the building is 40 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 that the angle of elevation is measured from the horizontal line up to the line of sight to the top of the building.
  • 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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