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

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Question: A person is standing 50 meters away from a statue. If the angle of elevation to the top of the statue is 45 degrees, what is the height of the statue?

Options:

  1. 25 meters
  2. 50 meters
  3. 35 meters
  4. 45 meters

Correct Answer: 50 meters

Solution: 

Height = distance * tan(angle) = 50 * 1 = 50 meters.

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

Practice Questions

Q1
A person is standing 50 meters away from a statue. If the angle of elevation to the top of the statue is 45 degrees, what is the height of the statue?
  1. 25 meters
  2. 50 meters
  3. 35 meters
  4. 45 meters

Questions & Step-by-Step Solutions

A person is standing 50 meters away from a statue. If the angle of elevation to the top of the statue is 45 degrees, what is the height of the statue?
Correct Answer: 50 meters
  • Step 1: Understand the situation. A person is standing 50 meters away from a statue.
  • Step 2: Know that the angle of elevation to the top of the statue is 45 degrees.
  • Step 3: Remember that the angle of elevation is the angle formed between the horizontal line (the ground) and the line of sight to the top of the statue.
  • Step 4: Use the tangent function in trigonometry, which relates the angle to the opposite side (height of the statue) and the adjacent side (distance from the statue).
  • Step 5: The formula for height is: Height = distance * tan(angle).
  • Step 6: Plug in the values: Height = 50 meters * tan(45 degrees).
  • Step 7: Know that tan(45 degrees) equals 1.
  • Step 8: Calculate the height: Height = 50 * 1 = 50 meters.
  • Step 9: Conclude that the height of the statue is 50 meters.
  • Trigonometry – The problem involves using the tangent function to relate the height of the statue to the distance from the observer and the angle of elevation.
  • Angle of Elevation – Understanding that the angle of elevation is measured from the horizontal line of sight to the top of the object.
  • Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the statue is the opposite side, the distance is the adjacent side, and the angle is given.
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