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A person is standing 12 meters away from a vertical pole. If the angle of elevat

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Question: A person is standing 12 meters away from a vertical pole. If the angle of elevation to the top of the pole is 45 degrees, what is the height of the pole?

Options:

  1. 12 meters
  2. 6 meters
  3. 8 meters
  4. 10 meters

Correct Answer: 12 meters

Solution: 

Using tan(45) = height / 12, height = 12 * tan(45) = 12 * 1 = 12 meters.

A person is standing 12 meters away from a vertical pole. If the angle of elevat

Practice Questions

Q1
A person is standing 12 meters away from a vertical pole. If the angle of elevation to the top of the pole is 45 degrees, what is the height of the pole?
  1. 12 meters
  2. 6 meters
  3. 8 meters
  4. 10 meters

Questions & Step-by-Step Solutions

A person is standing 12 meters away from a vertical pole. If the angle of elevation to the top of the pole is 45 degrees, what is the height of the pole?
  • Step 1: Understand the situation. A person is standing 12 meters away from a vertical pole.
  • Step 2: Identify the angle of elevation to the top of the pole, which is 45 degrees.
  • Step 3: Recall the definition of the tangent function in a right triangle: tan(angle) = opposite side / adjacent side.
  • Step 4: In this case, the 'opposite side' is the height of the pole, and the 'adjacent side' is the distance from the person to the pole, which is 12 meters.
  • Step 5: Write the equation using the tangent function: tan(45 degrees) = height / 12.
  • Step 6: Know that tan(45 degrees) equals 1. So, the equation becomes: 1 = height / 12.
  • Step 7: To find the height, multiply both sides of the equation by 12: height = 12 * 1.
  • Step 8: Calculate the height: height = 12 meters.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the pole and the distance from the pole.
  • Angle of Elevation – Understanding how the angle of elevation relates to the height and distance in a right triangle.
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