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From a point on the ground, the angle of elevation to the top of a 12-meter tall

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Question: From a point on the ground, the angle of elevation to the top of a 12-meter tall pole is 60 degrees. How far is the point from the base of the pole?

Options:

  1. 6 meters
  2. 10 meters
  3. 12 meters
  4. 15 meters

Correct Answer: 6 meters

Solution: 

Distance = height / tan(60) = 12 / √3 ≈ 6 meters.

From a point on the ground, the angle of elevation to the top of a 12-meter tall

Practice Questions

Q1
From a point on the ground, the angle of elevation to the top of a 12-meter tall pole is 60 degrees. How far is the point from the base of the pole?
  1. 6 meters
  2. 10 meters
  3. 12 meters
  4. 15 meters

Questions & Step-by-Step Solutions

From a point on the ground, the angle of elevation to the top of a 12-meter tall pole is 60 degrees. How far is the point from the base of the pole?
Correct Answer: 6 meters
  • Step 1: Understand the problem. We have a pole that is 12 meters tall and we want to find out how far away we are from the base of the pole.
  • Step 2: Identify the angle of elevation. The angle of elevation to the top of the pole is 60 degrees.
  • Step 3: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the pole) divided by the adjacent side (distance from the pole).
  • Step 4: Write the formula. We can write this as: tan(60 degrees) = height / distance.
  • Step 5: Plug in the values. We know the height is 12 meters, so we have: tan(60) = 12 / distance.
  • Step 6: Rearrange the formula to find distance. This gives us: distance = height / tan(60).
  • Step 7: Calculate tan(60 degrees). The value of tan(60 degrees) is √3.
  • Step 8: Substitute tan(60) into the formula. Now we have: distance = 12 / √3.
  • Step 9: Calculate the distance. This simplifies to approximately 6 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 base.
  • Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the pole, the ground, and the line of sight.
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