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A man is standing on the ground and observes the top of a building at an angle o

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Question: A man is standing on the ground and observes the top of a building at an angle of elevation of 60 degrees. If he is 50 m away from the building, what is the height of the building?

Options:

  1. 25 m
  2. 43.3 m
  3. 50 m
  4. 86.6 m

Correct Answer: 43.3 m

Solution: 

Using tan(60°) = height/50, we have √3 = height/50. Therefore, height = 50√3 ≈ 86.6 m.

A man is standing on the ground and observes the top of a building at an angle o

Practice Questions

Q1
A man is standing on the ground and observes the top of a building at an angle of elevation of 60 degrees. If he is 50 m away from the building, what is the height of the building?
  1. 25 m
  2. 43.3 m
  3. 50 m
  4. 86.6 m

Questions & Step-by-Step Solutions

A man is standing on the ground and observes the top of a building at an angle of elevation of 60 degrees. If he is 50 m away from the building, what is the height of the building?
  • Step 1: Understand the problem. A man is looking at the top of a building from a distance of 50 meters.
  • Step 2: Identify the angle of elevation. The angle at which he looks up to see the top of the building is 60 degrees.
  • Step 3: Recall 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 building).
  • Step 4: Set up the equation using the tangent function. We have tan(60°) = height / 50.
  • Step 5: Find the value of tan(60°). The value of tan(60°) is √3.
  • Step 6: Substitute the value into the equation. Now we have √3 = height / 50.
  • Step 7: Solve for the height. Multiply both sides by 50 to get height = 50√3.
  • Step 8: Calculate the height. Using a calculator, 50√3 is approximately 86.6 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 observer, the top of the building, and the base of the building.
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