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A person is standing 50 meters away from a building. If the angle of elevation t

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Question: A person is standing 50 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?

Options:

  1. 25 meters
  2. 50 meters
  3. 75 meters
  4. 100 meters

Correct Answer: 25 meters

Solution: 

Height = distance * tan(angle) = 50 * (1/√3) = 50/√3 meters.

A person is standing 50 meters away from a building. If the angle of elevation t

Practice Questions

Q1
A person is standing 50 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?
  1. 25 meters
  2. 50 meters
  3. 75 meters
  4. 100 meters

Questions & Step-by-Step Solutions

A person is standing 50 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?
Correct Answer: 28.87 meters
  • Step 1: Understand the problem. You have a person standing 50 meters away from a building and looking up at the top of the building at an angle of 30 degrees.
  • Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the building, the other side is the distance from the person to the building (50 meters), and the angle between the ground and the line of sight to the top of the building is 30 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 building) divided by the adjacent side (distance from the person to the building).
  • Step 4: Write the formula. The formula is: height = distance * tan(angle). Here, distance is 50 meters and angle is 30 degrees.
  • Step 5: Find the value of tan(30 degrees). The tangent of 30 degrees is 1/√3.
  • Step 6: Substitute the values into the formula. So, height = 50 * (1/√3).
  • Step 7: Calculate the height. This gives you height = 50/√3 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.
  • 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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