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A helicopter is hovering at a height of 100 meters. If a person on the ground is

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Question: A helicopter is hovering at a height of 100 meters. If a person on the ground is 80 meters away from the point directly below the helicopter, what is the angle of elevation from the person to the helicopter?

Options:

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

Correct Answer: 53.13 degrees

Solution: 

tan(θ) = height/distance = 100/80; θ = tan^(-1)(1.25) = 53.13 degrees.

A helicopter is hovering at a height of 100 meters. If a person on the ground is

Practice Questions

Q1
A helicopter is hovering at a height of 100 meters. If a person on the ground is 80 meters away from the point directly below the helicopter, what is the angle of elevation from the person to the helicopter?
  1. 36.87 degrees
  2. 45 degrees
  3. 53.13 degrees
  4. 60 degrees

Questions & Step-by-Step Solutions

A helicopter is hovering at a height of 100 meters. If a person on the ground is 80 meters away from the point directly below the helicopter, what is the angle of elevation from the person to the helicopter?
  • Step 1: Identify the height of the helicopter above the ground, which is 100 meters.
  • Step 2: Identify the horizontal distance from the person on the ground to the point directly below the helicopter, which is 80 meters.
  • Step 3: Use the formula for the tangent of the angle of elevation (θ), which is tan(θ) = height/distance.
  • Step 4: Substitute the values into the formula: tan(θ) = 100 meters / 80 meters.
  • Step 5: Calculate the value: tan(θ) = 1.25.
  • Step 6: To find the angle θ, use the inverse tangent function: θ = tan^(-1)(1.25).
  • Step 7: Calculate θ using a calculator: θ ≈ 53.13 degrees.
  • Trigonometry – The problem involves using the tangent function to find the angle of elevation based on the height of the helicopter and the horizontal 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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