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A person is standing 45 meters away from a building. If the angle of elevation t

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Question: A person is standing 45 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. 30 meters
  2. 45 meters
  3. 60 meters
  4. 75 meters

Correct Answer: 45 meters

Solution: 

Height = distance * tan(angle) = 45 * 1 = 45 meters.

A person is standing 45 meters away from a building. If the angle of elevation t

Practice Questions

Q1
A person is standing 45 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. 30 meters
  2. 45 meters
  3. 60 meters
  4. 75 meters

Questions & Step-by-Step Solutions

A person is standing 45 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: 45 meters
  • Step 1: Understand the problem. You have a person standing 45 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: For an angle of 45 degrees, the tangent value is 1. This means height = distance.
  • Step 5: Calculate the height of the building using the formula: Height = distance * tan(angle).
  • Step 6: Substitute the values: Height = 45 meters * tan(45 degrees).
  • Step 7: Since tan(45 degrees) = 1, the calculation becomes Height = 45 meters * 1.
  • Step 8: Therefore, the height of the building is 45 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 – Understanding the relationship between the sides of a right triangle formed by the height of the building, the distance from the building, and the angle of elevation.
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