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From a point on the ground, the angle of elevation to the top of a 15-meter tall

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Question: From a point on the ground, the angle of elevation to the top of a 15-meter tall building is 45 degrees. How far is the point from the base of the building?

Options:

  1. 15 meters
  2. 30 meters
  3. 10 meters
  4. 20 meters

Correct Answer: 15 meters

Solution: 

Using tan(45°) = height/distance, distance = height/tan(45°) = 15/1 = 15 meters.

From a point on the ground, the angle of elevation to the top of a 15-meter tall

Practice Questions

Q1
From a point on the ground, the angle of elevation to the top of a 15-meter tall building is 45 degrees. How far is the point from the base of the building?
  1. 15 meters
  2. 30 meters
  3. 10 meters
  4. 20 meters

Questions & Step-by-Step Solutions

From a point on the ground, the angle of elevation to the top of a 15-meter tall building is 45 degrees. How far is the point from the base of the building?
  • Step 1: Understand that the angle of elevation is the angle formed between the ground and the line of sight to the top of the building.
  • Step 2: Identify the height of the building, which is 15 meters.
  • Step 3: Recognize that the angle of elevation is 45 degrees.
  • Step 4: Use the tangent function, which relates the angle to the opposite side (height of the building) and the adjacent side (distance from the building).
  • Step 5: Write the formula: tan(angle) = height/distance.
  • Step 6: Substitute the known values into the formula: tan(45°) = 15/distance.
  • Step 7: Know that tan(45°) equals 1, so the equation becomes 1 = 15/distance.
  • Step 8: Rearrange the equation to find distance: distance = 15/1.
  • Step 9: Calculate the distance, which equals 15 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 is crucial for visualizing the problem and applying the correct trigonometric function.
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