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A building is 80 meters tall. From a point 60 meters away from the base of the b

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Question: A building is 80 meters tall. From a point 60 meters away from the base of the building, what is the angle of elevation to the top of the building?

Options:

  1. 30 degrees
  2. 36.87 degrees
  3. 45 degrees
  4. 53.13 degrees

Correct Answer: 36.87 degrees

Solution: 

tan(θ) = height/distance = 80/60, θ = tan⁻¹(4/3) ≈ 36.87 degrees.

A building is 80 meters tall. From a point 60 meters away from the base of the b

Practice Questions

Q1
A building is 80 meters tall. From a point 60 meters away from the base of the building, what is the angle of elevation to the top of the building?
  1. 30 degrees
  2. 36.87 degrees
  3. 45 degrees
  4. 53.13 degrees

Questions & Step-by-Step Solutions

A building is 80 meters tall. From a point 60 meters away from the base of the building, what is the angle of elevation to the top of the building?
Correct Answer: 36.87 degrees
  • Step 1: Identify the height of the building, which is 80 meters.
  • Step 2: Identify the distance from the point to the base of the building, which is 60 meters.
  • Step 3: Understand that the angle of elevation (θ) is the angle formed between the line of sight to the top of the building and the horizontal line from the point to the base of the building.
  • 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). The formula is tan(θ) = height/distance.
  • Step 5: Plug in the values: tan(θ) = 80 meters (height) / 60 meters (distance).
  • Step 6: Simplify the fraction: tan(θ) = 4/3.
  • Step 7: To find the angle θ, use the inverse tangent function: θ = tan⁻¹(4/3).
  • Step 8: Calculate θ using a calculator: θ ≈ 36.87 degrees.
  • Trigonometry – The problem involves using the tangent function to find the angle of elevation based on the height of the building and the distance from the observer.
  • Right Triangle Properties – Understanding the relationship between the sides of a right triangle and the angles formed, specifically in the context of elevation.
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