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From a point A, the angle of elevation of the top of a building is 45 degrees. I

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Question: From a point A, the angle of elevation of the top of a building is 45 degrees. If the height of the building is 20 meters, how far is point A from the base of the building?

Options:

  1. 10 m
  2. 20 m
  3. 30 m
  4. 40 m

Correct Answer: 20 m

Solution: 

Using tan(45°) = height/distance, we have 1 = 20/distance. Therefore, distance = 20 m.

From a point A, the angle of elevation of the top of a building is 45 degrees. I

Practice Questions

Q1
From a point A, the angle of elevation of the top of a building is 45 degrees. If the height of the building is 20 meters, how far is point A from the base of the building?
  1. 10 m
  2. 20 m
  3. 30 m
  4. 40 m

Questions & Step-by-Step Solutions

From a point A, the angle of elevation of the top of a building is 45 degrees. If the height of the building is 20 meters, how far is point A from the base of the building?
  • Step 1: Understand that the angle of elevation is the angle formed between the horizontal line from point A and the line of sight to the top of the building.
  • Step 2: Note that the angle of elevation is 45 degrees.
  • Step 3: Recall that the height of the building is 20 meters.
  • Step 4: Use the tangent function, which relates the angle of elevation to the height of the building and the distance from point A to the base of the building.
  • Step 5: Write the formula: tan(angle) = height / distance.
  • Step 6: Substitute the known values into the formula: tan(45°) = 20 / distance.
  • Step 7: Know that tan(45°) equals 1.
  • Step 8: Set up the equation: 1 = 20 / distance.
  • Step 9: Rearrange the equation to find distance: distance = 20 / 1.
  • Step 10: Calculate the distance: distance = 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 point to the base.
  • Angle of Elevation – Understanding the concept of angle of elevation and how it relates to right triangles.
  • Right Triangle Properties – Applying properties of right triangles to solve for unknown lengths using trigonometric ratios.
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