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A building is 24 meters tall. If a person is standing 32 meters away from the ba

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Question: A building is 24 meters tall. If a person is standing 32 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. 45 degrees
  3. 60 degrees
  4. 75 degrees

Correct Answer: 60 degrees

Solution: 

tan(θ) = height/distance = 24/32 = 0.75; θ = tan^(-1)(0.75) ≈ 36.87 degrees.

A building is 24 meters tall. If a person is standing 32 meters away from the ba

Practice Questions

Q1
A building is 24 meters tall. If a person is standing 32 meters away from the base of the building, what is the angle of elevation to the top of the building?
  1. 30 degrees
  2. 45 degrees
  3. 60 degrees
  4. 75 degrees

Questions & Step-by-Step Solutions

A building is 24 meters tall. If a person is standing 32 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 24 meters.
  • Step 2: Identify the distance from the person to the base of the building, which is 32 meters.
  • Step 3: Use the tangent function, which relates the angle of elevation (θ) to the height and distance: tan(θ) = height/distance.
  • Step 4: Substitute the values into the formula: tan(θ) = 24/32.
  • Step 5: Simplify the fraction: 24/32 = 0.75.
  • Step 6: To find the angle θ, use the inverse tangent function: θ = tan^(-1)(0.75).
  • Step 7: Calculate θ using a calculator: 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 – It assesses the ability to apply the inverse tangent function to find the angle from the tangent value.
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