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A person is 50 meters away from a cliff. If the angle of elevation to the top of

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Question: A person is 50 meters away from a cliff. If the angle of elevation to the top of the cliff is 30 degrees, what is the height of the cliff?

Options:

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

Correct Answer: 25√3 meters

Solution: 

Height = distance * tan(30) = 50 * (1/√3) = 50/√3 = 25√3 meters.

A person is 50 meters away from a cliff. If the angle of elevation to the top of

Practice Questions

Q1
A person is 50 meters away from a cliff. If the angle of elevation to the top of the cliff is 30 degrees, what is the height of the cliff?
  1. 25√3 meters
  2. 50√3 meters
  3. 75√3 meters
  4. 100√3 meters

Questions & Step-by-Step Solutions

A person is 50 meters away from a cliff. If the angle of elevation to the top of the cliff is 30 degrees, what is the height of the cliff?
  • Step 1: Understand the problem. You have a person standing 50 meters away from a cliff and looking up at the top of the cliff at an angle of 30 degrees.
  • Step 2: Visualize the situation. 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 (50 meters), and the angle between the ground and the line of sight to the top of the cliff is 30 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 cliff) divided by the adjacent side (distance to the cliff). So, tan(30 degrees) = height / 50 meters.
  • Step 4: Find the value of tan(30 degrees). The value of tan(30 degrees) is 1/√3.
  • Step 5: Set up the equation. Now, you can write the equation: height = 50 * tan(30 degrees).
  • Step 6: Substitute the value of tan(30 degrees) into the equation. This gives you height = 50 * (1/√3).
  • Step 7: Simplify the equation. This means height = 50/√3.
  • Step 8: To make it easier to understand, you can multiply the numerator and denominator by √3. This gives you height = (50√3)/3.
  • Step 9: Calculate the height. The final height of the cliff is approximately 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 horizontal distance.
  • Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the cliff, the distance from the cliff, and the angle of elevation.
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