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A building is 40 m tall. From a point on the ground, the angle of elevation to t

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Question: A building is 40 m tall. From a point on the ground, the angle of elevation to the top of the building is 45 degrees. How far is the point from the base of the building? (2020)

Options:

  1. 20 m
  2. 30 m
  3. 40 m
  4. 50 m

Correct Answer: 40 m

Exam Year: 2020

Solution: 

Distance = height / tan(angle) = 40 / tan(45) = 40 / 1 = 40 m.

A building is 40 m tall. From a point on the ground, the angle of elevation to t

Practice Questions

Q1
A building is 40 m tall. From a point on the ground, the angle of elevation to the top of the building is 45 degrees. How far is the point from the base of the building? (2020)
  1. 20 m
  2. 30 m
  3. 40 m
  4. 50 m

Questions & Step-by-Step Solutions

A building is 40 m tall. From a point on the ground, the angle of elevation to the top of the building is 45 degrees. How far is the point from the base of the building? (2020)
  • Step 1: Understand the problem. We have a building that is 40 meters tall.
  • Step 2: Identify the angle of elevation from the ground to the top of the building, which is 45 degrees.
  • Step 3: Recall the relationship between the height of the building, the distance from the point to the base of the building, and the angle of elevation. We can use the tangent function.
  • Step 4: Write down the formula for distance: Distance = height / tan(angle).
  • Step 5: Substitute the values into the formula: Distance = 40 m / tan(45 degrees).
  • Step 6: Calculate tan(45 degrees), which is equal to 1.
  • Step 7: Now, substitute tan(45) into the formula: Distance = 40 m / 1.
  • Step 8: Perform the division: Distance = 40 m.
  • Step 9: Conclude that the point is 40 meters away from the base of the building.
  • Trigonometry – The problem involves using the tangent function to relate the height of the building to the distance from the point on the ground.
  • Angle of Elevation – Understanding the angle of elevation is crucial for visualizing the relationship between the height of the building and the distance from the observer.
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