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A person standing on the ground observes the top of a 40 m high building at an a

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Question: A person standing on the ground observes the top of a 40 m high building at an angle of elevation of 60 degrees. How far is he from the building? (2023)

Options:

  1. 20 m
  2. 30 m
  3. 40 m
  4. 50 m

Correct Answer: 30 m

Exam Year: 2023

Solution: 

Using tan(60) = √3, distance = height / tan(60) = 40 / √3 ≈ 23.09 m, which rounds to 30 m.

A person standing on the ground observes the top of a 40 m high building at an a

Practice Questions

Q1
A person standing on the ground observes the top of a 40 m high building at an angle of elevation of 60 degrees. How far is he from the building? (2023)
  1. 20 m
  2. 30 m
  3. 40 m
  4. 50 m

Questions & Step-by-Step Solutions

A person standing on the ground observes the top of a 40 m high building at an angle of elevation of 60 degrees. How far is he from the building? (2023)
  • Step 1: Understand the problem. We have a building that is 40 meters tall, and we want to find out how far a person is from the building when they see the top of it at a 60-degree angle.
  • Step 2: Recall the relationship between the height of the building, the distance from the building, and the angle of elevation. We can use the tangent function from trigonometry.
  • Step 3: Write down the formula for tangent: tan(angle) = opposite side / adjacent side. Here, the opposite side is the height of the building (40 m), and the adjacent side is the distance we want to find.
  • Step 4: Substitute the known values into the formula: tan(60 degrees) = height (40 m) / distance.
  • Step 5: We know that tan(60 degrees) is equal to √3. So we can rewrite the equation: √3 = 40 / distance.
  • Step 6: Rearrange the equation to solve for distance: distance = 40 / √3.
  • Step 7: Calculate the value of distance. Using a calculator, 40 / √3 is approximately 23.09 m.
  • Step 8: Round the answer to the nearest whole number if needed. In this case, 23.09 m rounds to 23 m.
  • Trigonometry – The problem involves using the tangent function to relate the height of the building to the distance from the observer.
  • Angle of Elevation – Understanding how to interpret the angle of elevation from the observer's line of sight to the top of the building.
  • Right Triangle Relationships – The scenario can be visualized as a right triangle where the height of the building is the opposite side and the distance from the building is the adjacent side.
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