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From a point on the ground, the angle of elevation to the top of a building is 4

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Question: From a point on the ground, the angle of elevation to the top of a building is 45 degrees. If the point is 20 meters away from the building, what is the height of the building?

Options:

  1. 20 meters
  2. 10 meters
  3. 30 meters
  4. 25 meters

Correct Answer: 20 meters

Solution: 

Height = distance * tan(45) = 20 * 1 = 20 meters.

From a point on the ground, the angle of elevation to the top of a building is 4

Practice Questions

Q1
From a point on the ground, the angle of elevation to the top of a building is 45 degrees. If the point is 20 meters away from the building, what is the height of the building?
  1. 20 meters
  2. 10 meters
  3. 30 meters
  4. 25 meters

Questions & Step-by-Step Solutions

From a point on the ground, the angle of elevation to the top of a building is 45 degrees. If the point is 20 meters away from the building, what is the height of the building?
Correct Answer: 20 meters
  • Step 1: Understand that the angle of elevation is the angle formed between the horizontal line from your point on the ground and the line of sight to the top of the building.
  • Step 2: Recognize that when the angle of elevation is 45 degrees, the height of the building is equal to the distance from the point to the building.
  • Step 3: Note that the distance from the point on the ground to the building is given as 20 meters.
  • Step 4: Use the tangent function, which relates the angle of elevation to the height and distance. For 45 degrees, tan(45) equals 1.
  • Step 5: Calculate the height of the building using the formula: Height = distance * tan(angle). Here, Height = 20 meters * tan(45 degrees).
  • Step 6: Since tan(45 degrees) is 1, the calculation simplifies to Height = 20 meters * 1.
  • Step 7: Conclude that the height of the building is 20 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 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.
  • 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 45 degrees.
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