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A person standing 15 meters away from a statue sees the top of the statue at an

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Question: A person standing 15 meters away from a statue sees the top of the statue at an angle of elevation of 45 degrees. What is the height of the statue?

Options:

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

Correct Answer: 15 meters

Solution: 

Using tan(45) = height/distance, height = distance * tan(45) = 15 * 1 = 15 meters.

A person standing 15 meters away from a statue sees the top of the statue at an

Practice Questions

Q1
A person standing 15 meters away from a statue sees the top of the statue at an angle of elevation of 45 degrees. What is the height of the statue?
  1. 15 meters
  2. 20 meters
  3. 25 meters
  4. 30 meters

Questions & Step-by-Step Solutions

A person standing 15 meters away from a statue sees the top of the statue at an angle of elevation of 45 degrees. What is the height of the statue?
  • Step 1: Understand that the person is standing 15 meters away from the statue.
  • Step 2: Know that the angle of elevation to the top of the statue is 45 degrees.
  • Step 3: Recall that the tangent of an angle in a right triangle is the ratio of the opposite side (height of the statue) to the adjacent side (distance from the statue).
  • Step 4: Write the formula: tan(angle) = height / distance.
  • Step 5: Substitute the known values into the formula: tan(45 degrees) = height / 15 meters.
  • Step 6: Know that tan(45 degrees) equals 1.
  • Step 7: Set up the equation: 1 = height / 15 meters.
  • Step 8: Multiply both sides by 15 meters to solve for height: height = 15 meters * 1.
  • Step 9: Conclude that the height of the statue is 15 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 observer.
  • Angle of Elevation – Understanding how the angle of elevation from a point to the top of an object can be used to calculate height.
  • Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the statue is the opposite side, the distance from the observer is the adjacent side, and the angle of elevation is the angle between them.
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