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A person is standing 25 meters away from a building and measures the angle of el

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Question: A person is standing 25 meters away from a building and measures the angle of elevation to the top of the building as 36.87 degrees. What is the height of the building?

Options:

  1. 15 meters
  2. 20 meters
  3. 10 meters
  4. 25 meters

Correct Answer: 15 meters

Solution: 

Let h be the height of the building. tan(36.87°) = h/25. Therefore, h = 25 * tan(36.87°) = 25 * 0.75 = 18.75 meters.

A person is standing 25 meters away from a building and measures the angle of el

Practice Questions

Q1
A person is standing 25 meters away from a building and measures the angle of elevation to the top of the building as 36.87 degrees. What is the height of the building?
  1. 15 meters
  2. 20 meters
  3. 10 meters
  4. 25 meters

Questions & Step-by-Step Solutions

A person is standing 25 meters away from a building and measures the angle of elevation to the top of the building as 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 measuring the angle of elevation to the top of the building as 36.87 degrees.
  • Step 2: Identify what you need to find. You need to calculate the height of the building, which we will call 'h'.
  • Step 3: Use the tangent function. The tangent of an angle in a right triangle is the opposite side (height of the building) divided by the adjacent side (distance from the building).
  • Step 4: Write the equation using the tangent function. For the angle of 36.87 degrees, the equation is: tan(36.87°) = h / 25.
  • Step 5: Rearrange the equation to solve for h. Multiply both sides by 25: h = 25 * tan(36.87°).
  • Step 6: Calculate tan(36.87°). The value of tan(36.87°) is approximately 0.75.
  • Step 7: Substitute the value of tan(36.87°) into the equation: h = 25 * 0.75.
  • Step 8: Perform the multiplication: h = 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 it.
  • Angle of Elevation – Understanding how to apply the angle of elevation in a right triangle to find the height of an object.
  • Right Triangle Properties – Utilizing the properties of right triangles to solve for unknown sides using trigonometric ratios.
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