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A person is standing 25 meters away from a vertical pole. If the angle of elevat

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Question: A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 36.87 degrees, what is the height of the pole?

Options:

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

Correct Answer: 15 m

Solution: 

Using tan(36.87°) = height/distance, we have height = distance * tan(36.87°) = 25 * 0.75 = 15 m.

A person is standing 25 meters away from a vertical pole. If the angle of elevat

Practice Questions

Q1
A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 36.87 degrees, what is the height of the pole?
  1. 15 m
  2. 20 m
  3. 25 m
  4. 30 m

Questions & Step-by-Step Solutions

A person is standing 25 meters away from a vertical pole. If the angle of elevation to the top of the pole is 36.87 degrees, what is the height of the pole?
  • Step 1: Understand the problem. You have a person standing 25 meters away from a pole and you need to find the height of the pole.
  • Step 2: Identify the angle of elevation. The angle of elevation to the top of the pole is given as 36.87 degrees.
  • Step 3: Use the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side (height of the pole) to the adjacent side (distance from the pole).
  • Step 4: Write the formula. The formula is tan(angle) = height / distance.
  • Step 5: Plug in the values. Here, angle = 36.87 degrees and distance = 25 meters. So, tan(36.87°) = height / 25.
  • Step 6: Find tan(36.87°). The value of tan(36.87°) is approximately 0.75.
  • Step 7: Rearrange the formula to find height. height = distance * tan(36.87°).
  • Step 8: Calculate the height. height = 25 * 0.75 = 18.75 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.
  • 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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