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A building is 120 meters tall. From a point 80 meters away from the base of the

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Question: A building is 120 meters tall. From a point 80 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 = 120/80 = 1.5, θ = tan⁻¹(1.5) ≈ 60 degrees.

A building is 120 meters tall. From a point 80 meters away from the base of the

Practice Questions

Q1
A building is 120 meters tall. From a point 80 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 120 meters tall. From a point 80 meters away from the base of the building, what is the angle of elevation to the top of the building?
Correct Answer: 60 degrees
  • Step 1: Identify the height of the building, which is 120 meters.
  • Step 2: Identify the distance from the point to the base of the building, which is 80 meters.
  • Step 3: Use the formula for the tangent of the angle of elevation: tan(θ) = height/distance.
  • Step 4: Substitute the values into the formula: tan(θ) = 120/80.
  • Step 5: Simplify the fraction: 120/80 = 1.5.
  • Step 6: To find the angle θ, use the inverse tangent function: θ = tan⁻¹(1.5).
  • Step 7: Calculate θ using a calculator: θ ≈ 60 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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