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A person is looking at the top of a hill from a distance of 50 meters. If the an

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Question: A person is looking at the top of a hill from a distance of 50 meters. If the angle of elevation is 30 degrees, what is the height of the hill?

Options:

  1. 25 meters
  2. 50 meters
  3. 75 meters
  4. 100 meters

Correct Answer: 25 meters

Solution: 

Height = distance * tan(30) = 50 * (1/√3) = 50/√3 ≈ 28.87 meters.

A person is looking at the top of a hill from a distance of 50 meters. If the an

Practice Questions

Q1
A person is looking at the top of a hill from a distance of 50 meters. If the angle of elevation is 30 degrees, what is the height of the hill?
  1. 25 meters
  2. 50 meters
  3. 75 meters
  4. 100 meters

Questions & Step-by-Step Solutions

A person is looking at the top of a hill from a distance of 50 meters. If the angle of elevation is 30 degrees, what is the height of the hill?
  • Step 1: Understand the problem. We need to find the height of a hill when looking from a distance of 50 meters at an angle of elevation of 30 degrees.
  • Step 2: Recall the relationship between the angle of elevation, the height of the hill, and the distance from the hill. We can use the tangent function: tan(angle) = opposite/adjacent.
  • Step 3: In this case, the 'opposite' side is the height of the hill (which we want to find), and the 'adjacent' side is the distance from the person to the hill (50 meters).
  • Step 4: Set up the equation using the tangent function: tan(30 degrees) = height / 50 meters.
  • Step 5: We know that tan(30 degrees) is equal to 1/√3.
  • Step 6: Substitute tan(30 degrees) into the equation: 1/√3 = height / 50.
  • Step 7: To find the height, multiply both sides of the equation by 50: height = 50 * (1/√3).
  • Step 8: Calculate the height: height = 50/√3.
  • Step 9: To get a numerical value, you can approximate 50/√3, which is about 28.87 meters.
  • Trigonometry – The problem tests the understanding of basic trigonometric functions, specifically the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle.
  • Right Triangle Properties – The question involves applying properties of right triangles to find the height of the hill using the given distance and angle.
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