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A person standing 30 meters away from a building observes the angle of elevation

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Question: A person standing 30 meters away from a building observes the angle of elevation to the top of the building as 60 degrees. What is the height of the building?

Options:

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

Correct Answer: 15√3 meters

Solution: 

Using tan(60) = height/30, height = 30 * √3 = 15√3 meters.

A person standing 30 meters away from a building observes the angle of elevation

Practice Questions

Q1
A person standing 30 meters away from a building observes the angle of elevation to the top of the building as 60 degrees. What is the height of the building?
  1. 15√3 meters
  2. 30 meters
  3. 20 meters
  4. 25 meters

Questions & Step-by-Step Solutions

A person standing 30 meters away from a building observes the angle of elevation to the top of the building as 60 degrees. What is the height of the building?
  • Step 1: Understand the problem. You have a person standing 30 meters away from a building and looking up at the top of the building, forming an angle of 60 degrees with the ground.
  • Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the building (which we want to find), the other side is the distance from the person to the building (30 meters), and the angle at the person's position is 60 degrees.
  • Step 3: Use the tangent function. In a right triangle, the tangent of an angle is the opposite side (height of the building) divided by the adjacent side (distance from the person to the building). So, tan(60 degrees) = height / 30.
  • Step 4: Find the value of tan(60 degrees). The value of tan(60 degrees) is √3.
  • Step 5: Set up the equation. Now, we can write the equation as √3 = height / 30.
  • Step 6: Solve for height. Multiply both sides of the equation by 30 to isolate height: height = 30 * √3.
  • Step 7: Calculate the height. The height of the building is 30 * √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 the observer.
  • Right Triangle Properties – Understanding the properties of right triangles is essential, as the scenario describes a right triangle formed by the observer, the top of the building, and the base of the building.
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