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A person standing 100 meters away from a hill observes the top of the hill at an

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Question: A person standing 100 meters away from a hill observes the top of the hill at an angle of elevation of 60 degrees. What is the height of the hill?

Options:

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

Correct Answer: 100√3

Solution: 

height = distance * tan(60) = 100 * √3 = 100√3 meters

A person standing 100 meters away from a hill observes the top of the hill at an

Practice Questions

Q1
A person standing 100 meters away from a hill observes the top of the hill at an angle of elevation of 60 degrees. What is the height of the hill?
  1. 100√3
  2. 50√3
  3. 75√3
  4. 25√3

Questions & Step-by-Step Solutions

A person standing 100 meters away from a hill observes the top of the hill at an angle of elevation of 60 degrees. What is the height of the hill?
Correct Answer: 173.21 meters
  • Step 1: Understand the problem. You have a person standing 100 meters away from a hill and looking up at the top of the hill.
  • Step 2: Identify the angle of elevation. The angle at which the person looks up to see the top of the hill is 60 degrees.
  • Step 3: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the hill) divided by the adjacent side (distance from the hill).
  • Step 4: Set up the equation. The formula is: height = distance * tan(angle). Here, distance is 100 meters and angle is 60 degrees.
  • Step 5: Calculate tan(60 degrees). The value of tan(60 degrees) is √3.
  • Step 6: Substitute the values into the equation. height = 100 * tan(60) = 100 * √3.
  • Step 7: Simplify the calculation. The height of the hill is 100√3 meters.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the hill and the distance from the observer.
  • Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the hill is the opposite side, the distance from the observer is the adjacent side, and the angle of elevation is given.
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