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A person standing 50 meters away from a building observes the top of the buildin

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Question: A person standing 50 meters 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. 25 meters
  2. 15√3 meters
  3. 10√3 meters
  4. 20 meters

Correct Answer: 15√3 meters

Solution: 

Height = distance * tan(30) = 50 * (1/√3) = 50/√3 = 15√3 meters

A person standing 50 meters away from a building observes the top of the buildin

Practice Questions

Q1
A person standing 50 meters 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. 25 meters
  2. 15√3 meters
  3. 10√3 meters
  4. 20 meters

Questions & Step-by-Step Solutions

A person standing 50 meters 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?
Correct Answer: 15√3 meters
  • Step 1: Understand the problem. A person is standing 50 meters away from a building and sees the top of the building at an angle of elevation of 30 degrees.
  • Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the building (opposite side), the other side is the distance from the person to the building (adjacent side), and the angle is 30 degrees.
  • Step 3: Use the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side (height of the building) to the adjacent side (distance from the person to the building). So, tan(30 degrees) = height / 50 meters.
  • Step 4: Find the value of tan(30 degrees). The value of tan(30 degrees) is 1/√3.
  • Step 5: Set up the equation. Replace tan(30 degrees) in the equation: height = 50 * tan(30 degrees). This becomes height = 50 * (1/√3).
  • Step 6: Calculate the height. Multiply 50 by (1/√3) to get height = 50/√3.
  • Step 7: Simplify the height. You can also express this as height = 15√3 meters by rationalizing the denominator.
  • Trigonometry – The problem tests the understanding of right triangle relationships, specifically using the tangent function to find the height of a building based on the angle of elevation.
  • Angle of Elevation – The question involves interpreting the angle of elevation from a horizontal line to the top of the building, which is crucial for applying trigonometric functions correctly.
  • Distance and Height Relationship – The relationship between the horizontal distance from the observer to the building and the height of the building is tested through the tangent function.
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