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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 75 degrees. What is the height of the cliff?

Options:

  1. 25√3 meters
  2. 25√2 meters
  3. 25√5 meters
  4. 25 meters

Correct Answer: 25√3 meters

Solution: 

Using tan(75°) = height / 25, height = 25 * tan(75°) ≈ 25 * 3.732 = 93.3 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 75 degrees. What is the height of the cliff?
  1. 25√3 meters
  2. 25√2 meters
  3. 25√5 meters
  4. 25 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 75 degrees. What is the height of the cliff?
  • Step 1: Understand the problem. You have a person standing 25 meters away from a cliff and looking up at the top of the cliff at an angle of 75 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 (25 meters), and the angle between the ground and the line of sight to the top of the cliff is 75 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 from the person to the cliff). So, tan(75°) = height / 25.
  • Step 4: Rearrange the equation to find the height. Multiply both sides by 25 to isolate height: height = 25 * tan(75°).
  • Step 5: Calculate tan(75°). You can use a calculator to find that tan(75°) is approximately 3.732.
  • Step 6: Multiply to find the height. Now calculate height = 25 * 3.732, which equals approximately 93.3 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 – Understanding the relationship between the sides of a right triangle formed by the height of the cliff, the distance from the cliff, and the line of sight.
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