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A person is standing 25 meters away from a cliff and sees the top of the cliff a

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Question: A person is standing 25 meters away from a cliff and sees the top of the cliff at an angle of elevation of 60 degrees. What is the height of the cliff?

Options:

  1. 25√3 meters
  2. 30 meters
  3. 20 meters
  4. 15 meters

Correct Answer: 25√3 meters

Solution: 

Using tan(60) = height/25, height = 25 * √3 = 25√3 meters.

A person is standing 25 meters away from a cliff and sees the top of the cliff a

Practice Questions

Q1
A person is standing 25 meters away from a cliff and sees the top of the cliff at an angle of elevation of 60 degrees. What is the height of the cliff?
  1. 25√3 meters
  2. 30 meters
  3. 20 meters
  4. 15 meters

Questions & Step-by-Step Solutions

A person is standing 25 meters away from a cliff and sees the top of the cliff at an angle of elevation of 60 degrees. What is the height of the cliff?
  • Step 1: Understand the situation. A person is standing 25 meters away from a cliff and looking up at the top of the cliff.
  • Step 2: Identify the angle of elevation. The angle at which the person looks up to see the top of the cliff is 60 degrees.
  • Step 3: Visualize the scenario. Imagine a right triangle where one side is the height of the cliff, the other side is the distance from the person to the cliff (25 meters), and the angle between the ground and the line of sight to the top of the cliff is 60 degrees.
  • Step 4: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the cliff) divided by the adjacent side (distance to the cliff). So, tan(60 degrees) = height / 25.
  • Step 5: Find the value of tan(60 degrees). The value of tan(60 degrees) is √3.
  • Step 6: Set up the equation. Now we have √3 = height / 25.
  • Step 7: Solve for height. Multiply both sides by 25 to get height = 25 * √3.
  • Step 8: Calculate the height. The height of the cliff is 25√3 meters.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the cliff and the distance from the cliff.
  • Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the cliff is the opposite side, the distance from the cliff is the adjacent side, and the angle of elevation is given.
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