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A person is standing 25 meters away from a building. If the angle of elevation t

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

Options:

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

Correct Answer: 15 meters

Solution: 

Using the tangent function, tan(36.87) = height / 25. Therefore, height = 25 * tan(36.87) = 25 * 0.75 = 18.75 meters.

A person is standing 25 meters away from a building. If the angle of elevation t

Practice Questions

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

Questions & Step-by-Step Solutions

A person is standing 25 meters away from a building. If the angle of elevation to the top of the building is 36.87 degrees, what is the height of the building?
  • Step 1: Understand the problem. You have a person standing 25 meters away from a building and looking up at the top of the building at an angle of 36.87 degrees.
  • Step 2: Identify the right triangle formed by the person, the top of the building, and the base of the building. The distance from the person to the building is one side (25 meters), the height of the building is the other side, and the line of sight to the top of the building is the hypotenuse.
  • Step 3: Use the tangent function, which relates the angle of elevation to the opposite side (height of the building) and the adjacent side (distance from the person to the building). The formula is: tan(angle) = opposite / adjacent.
  • Step 4: Plug in the values into the formula. Here, the angle is 36.87 degrees, the opposite side is the height (which we want to find), and the adjacent side is 25 meters. So, we write: tan(36.87) = height / 25.
  • Step 5: Rearrange the formula to solve for height. Multiply both sides by 25: height = 25 * tan(36.87).
  • Step 6: Calculate tan(36.87). From trigonometric tables or a calculator, tan(36.87) is approximately 0.75.
  • Step 7: Now substitute this value back into the equation: height = 25 * 0.75.
  • Step 8: Perform the multiplication: height = 25 * 0.75 = 18.75 meters.
  • Step 9: Conclude that the height of the building is 18.75 meters.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the building and the distance from the building.
  • Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the building, the distance from the building, and the angle of elevation.
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