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

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Question: A person is standing 50 meters away from a cliff. If the angle of elevation to the top of the cliff is 60 degrees, what is the height of the cliff?

Options:

  1. 25√3 meters
  2. 50 meters
  3. 30 meters
  4. 40 meters

Correct Answer: 25√3 meters

Solution: 

Using the tangent function, tan(60) = height / 50. Therefore, height = 50 * tan(60) = 50 * √3 = 50√3 meters.

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

Practice Questions

Q1
A person is standing 50 meters away from a cliff. If the angle of elevation to the top of the cliff is 60 degrees, what is the height of the cliff?
  1. 25√3 meters
  2. 50 meters
  3. 30 meters
  4. 40 meters

Questions & Step-by-Step Solutions

A person is standing 50 meters away from a cliff. If the angle of elevation to the top of the cliff is 60 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 60 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 60 degrees.
  • Step 3: Recall 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).
  • Step 4: Write the equation using the tangent function. For our angle of 60 degrees, we have: tan(60) = height / 50.
  • Step 5: Solve for the height. Rearranging the equation gives us height = 50 * tan(60).
  • Step 6: Calculate tan(60). The value of tan(60) is √3.
  • Step 7: Substitute tan(60) into the equation. Now we have height = 50 * √3.
  • Step 8: Final calculation. The height of the cliff is 50√3 meters.
  • Trigonometry – The problem tests the understanding of the tangent function in right triangles, specifically how to relate angles and side lengths.
  • Angle of Elevation – The question involves interpreting the angle of elevation from a horizontal line to a point above, which is crucial for solving the problem.
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