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A building is 25 meters tall. If a person is standing 20 meters away from the ba

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Question: A building is 25 meters tall. If a person is standing 20 meters away from the base of the building, what is the angle of elevation to the top of the building?

Options:

  1. 36.87 degrees
  2. 45 degrees
  3. 53.13 degrees
  4. 60 degrees

Correct Answer: 36.87 degrees

Solution: 

tan(θ) = height/distance = 25/20; θ = tan^(-1)(5/4) = 36.87 degrees.

A building is 25 meters tall. If a person is standing 20 meters away from the ba

Practice Questions

Q1
A building is 25 meters tall. If a person is standing 20 meters away from the base of the building, what is the angle of elevation to the top of the building?
  1. 36.87 degrees
  2. 45 degrees
  3. 53.13 degrees
  4. 60 degrees

Questions & Step-by-Step Solutions

A building is 25 meters tall. If a person is standing 20 meters away from the base of the building, what is the angle of elevation to the top of the building?
  • Step 1: Identify the height of the building, which is 25 meters.
  • Step 2: Identify the distance from the person to the base of the building, which is 20 meters.
  • Step 3: Understand that the angle of elevation (θ) is the angle formed between the line of sight from the person to the top of the building and the horizontal line from the person 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 person to the building). The formula is tan(θ) = height/distance.
  • Step 5: Plug in the values: tan(θ) = 25 meters (height) / 20 meters (distance).
  • Step 6: Simplify the fraction: tan(θ) = 25/20 = 5/4.
  • Step 7: To find the angle θ, use the inverse tangent function: θ = tan^(-1)(5/4).
  • Step 8: Calculate θ using a calculator to find that θ ≈ 36.87 degrees.
  • Trigonometry – The question tests the understanding of the tangent function in right triangles, specifically how to calculate the angle of elevation using the ratio of the opposite side (height of the building) to the adjacent side (distance from the building).
  • Inverse Trigonometric Functions – The solution requires the use of the inverse tangent function (tan^(-1)) to find the angle from the tangent ratio.
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