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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 30°, what is the height of the cliff?

Options:

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

Correct Answer: 25 meters

Solution: 

Height = distance * tan(30°) = 50 * (1/√3) = 25 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 30°, what is the height of the cliff?
  1. 25 meters
  2. 50 meters
  3. 75 meters
  4. 100 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 30°, what is the height of the cliff?
  • Step 1: Understand the problem. You have a person standing 50 meters away from a cliff and you need to find the height of the cliff.
  • Step 2: Identify the angle of elevation. The angle of elevation to the top of the cliff is given as 30°.
  • 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 cliff).
  • Step 4: Write the formula. The formula is: height = distance * tan(angle). Here, distance is 50 meters and angle is 30°.
  • Step 5: Find tan(30°). The value of tan(30°) is 1/√3.
  • Step 6: Substitute the values into the formula. Height = 50 * (1/√3).
  • Step 7: Calculate the height. Height = 50 / √3, which is approximately 25 meters.
  • Trigonometry – The question tests the understanding of basic trigonometric functions, specifically the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle.
  • Right Triangle Properties – It assesses the ability to apply properties of right triangles to find unknown lengths using angles.
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