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A person standing 40 m away from a building observes the top of the building at

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Question: A person standing 40 m away from a building observes the top of the building at an angle of elevation of 30 degrees. What is the height of the building?

Options:

  1. 10 m
  2. 20 m
  3. 30 m
  4. 40 m

Correct Answer: 20 m

Solution: 

Using tan(30°) = height/40, we have 1/√3 = height/40. Therefore, height = 40/√3 ≈ 23.1 m.

A person standing 40 m away from a building observes the top of the building at

Practice Questions

Q1
A person standing 40 m away from a building observes the top of the building at an angle of elevation of 30 degrees. What is the height of the building?
  1. 10 m
  2. 20 m
  3. 30 m
  4. 40 m

Questions & Step-by-Step Solutions

A person standing 40 m away from a building observes the top of the building at an angle of elevation of 30 degrees. What is the height of the building?
  • Step 1: Understand the problem. A person is standing 40 meters away from a building and sees the top of the building at an angle of 30 degrees.
  • Step 2: Visualize the situation. Draw a right triangle where one side is the height of the building, the other side is the distance from the person to the building (40 m), and the angle at the person's position is 30 degrees.
  • 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). So, tan(30°) = height / 40.
  • Step 4: Find the value of tan(30°). We know that tan(30°) = 1/√3.
  • Step 5: Set up the equation. Replace tan(30°) in the equation: 1/√3 = height / 40.
  • Step 6: Solve for height. Multiply both sides by 40: height = 40 * (1/√3).
  • Step 7: Calculate the height. This gives height = 40/√3.
  • Step 8: Approximate the height. Using a calculator, 40/√3 is approximately 23.1 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 observer, the top of the building, and the base of the building.
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