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From a point on the ground, the angle of elevation to the top of a 50-meter tall

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Question: From a point on the ground, the angle of elevation to the top of a 50-meter tall building is 45 degrees. How far is the point from the base of the building?

Options:

  1. 50 meters
  2. 25 meters
  3. 35 meters
  4. 40 meters

Correct Answer: 50 meters

Solution: 

distance = height / tan(45) = 50 / 1 = 50 meters

From a point on the ground, the angle of elevation to the top of a 50-meter tall

Practice Questions

Q1
From a point on the ground, the angle of elevation to the top of a 50-meter tall building is 45 degrees. How far is the point from the base of the building?
  1. 50 meters
  2. 25 meters
  3. 35 meters
  4. 40 meters

Questions & Step-by-Step Solutions

From a point on the ground, the angle of elevation to the top of a 50-meter tall building is 45 degrees. How far is the point from the base of the building?
Correct Answer: 50 meters
  • Step 1: Understand that the angle of elevation is the angle formed between the horizontal line from the observer's eye to the top of the building.
  • Step 2: Recognize that the height of the building is 50 meters.
  • Step 3: Note that the angle of elevation is 45 degrees.
  • Step 4: Use the tangent function, which relates the angle of elevation to the opposite side (height of the building) and the adjacent side (distance from the building).
  • Step 5: Recall that tan(45 degrees) equals 1.
  • Step 6: Set up the equation: distance = height / tan(angle).
  • Step 7: Substitute the values into the equation: distance = 50 meters / tan(45 degrees).
  • Step 8: Since tan(45 degrees) is 1, the equation simplifies to: distance = 50 meters / 1.
  • Step 9: Calculate the distance, which equals 50 meters.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height and distance from the building.
  • Angle of Elevation – Understanding how the angle of elevation relates to the height of the building and the horizontal distance from the observer.
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