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A person is standing 40 meters away from a statue and measures the angle of elev

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Question: A person is standing 40 meters away from a statue and measures the angle of elevation to the top of the statue as 53.13 degrees. What is the height of the statue?

Options:

  1. 30 meters
  2. 20 meters
  3. 25 meters
  4. 15 meters

Correct Answer: 30 meters

Solution: 

Let h be the height of the statue. tan(53.13°) = h/40. Therefore, h = 40 * tan(53.13°) = 40 * 1.6 = 64 meters.

A person is standing 40 meters away from a statue and measures the angle of elev

Practice Questions

Q1
A person is standing 40 meters away from a statue and measures the angle of elevation to the top of the statue as 53.13 degrees. What is the height of the statue?
  1. 30 meters
  2. 20 meters
  3. 25 meters
  4. 15 meters

Questions & Step-by-Step Solutions

A person is standing 40 meters away from a statue and measures the angle of elevation to the top of the statue as 53.13 degrees. What is the height of the statue?
  • Step 1: Understand the problem. You are standing 40 meters away from a statue and looking up at it.
  • Step 2: Identify the angle of elevation. The angle you are looking up at the top of the statue is 53.13 degrees.
  • Step 3: Use the tangent function. In a right triangle, the tangent of an angle is the opposite side (height of the statue) divided by the adjacent side (distance from the statue).
  • Step 4: Set up the equation. Let h be the height of the statue. The equation is tan(53.13°) = h / 40.
  • Step 5: Solve for h. Rearrange the equation to find h: h = 40 * tan(53.13°).
  • Step 6: Calculate tan(53.13°). The value of tan(53.13°) is approximately 1.6.
  • Step 7: Multiply to find the height. h = 40 * 1.6 = 64 meters.
  • Step 8: Conclusion. The height of the statue is 64 meters.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the statue and the distance from the statue.
  • Angle of Elevation – Understanding how to apply the angle of elevation in a right triangle to find the height of an object.
  • Right Triangle Properties – Utilizing the properties of right triangles to solve for unknown lengths using trigonometric ratios.
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