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A person standing 30 meters away from a cliff measures the angle of elevation to

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Question: A person standing 30 meters away from a cliff measures the angle of elevation to the top of the cliff as 60 degrees. How tall is the cliff?

Options:

  1. 15√3 meters
  2. 30 meters
  3. 20 meters
  4. 10√3 meters

Correct Answer: 15√3 meters

Solution: 

Let h be the height of the cliff. tan(60°) = h/30. Therefore, h = 30 * tan(60°) = 30 * √3 = 15√3 meters.

A person standing 30 meters away from a cliff measures the angle of elevation to

Practice Questions

Q1
A person standing 30 meters away from a cliff measures the angle of elevation to the top of the cliff as 60 degrees. How tall is the cliff?
  1. 15√3 meters
  2. 30 meters
  3. 20 meters
  4. 10√3 meters

Questions & Step-by-Step Solutions

A person standing 30 meters away from a cliff measures the angle of elevation to the top of the cliff as 60 degrees. How tall is the cliff?
  • Step 1: Understand the problem. You have a person standing 30 meters away from a cliff and measuring the angle of elevation to the top of the cliff as 60 degrees.
  • Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the cliff (h), the other side is the distance from the person to the cliff (30 meters), and the angle at the person's position is 60 degrees.
  • Step 3: Use the tangent function. In a right triangle, the tangent of an angle is the opposite side (height of the cliff) divided by the adjacent side (distance from the person to the cliff). So, tan(60°) = h / 30.
  • Step 4: Rearrange the equation to solve for h. Multiply both sides by 30: h = 30 * tan(60°).
  • Step 5: Calculate tan(60°). The value of tan(60°) is √3.
  • Step 6: Substitute the value of tan(60°) into the equation: h = 30 * √3.
  • Step 7: Simplify the expression. The height of the cliff is h = 30√3 meters.
  • Trigonometry – The problem involves using the tangent function to relate the height of the cliff to the distance from the cliff and the angle of elevation.
  • Angle of Elevation – Understanding how to interpret the angle of elevation in relation to a right triangle formed by the height of the cliff and the distance from the observer.
  • Right Triangle Properties – Applying properties of right triangles to solve for unknown lengths using trigonometric ratios.
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