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A person is standing 20 m away from a building and sees the top of the building

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Question: A person is standing 20 m away from a building and sees the top of the building at an angle of elevation of 45 degrees. What is the height of the building? (2019)

Options:

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

Correct Answer: 20 m

Exam Year: 2019

Solution: 

Height = distance * tan(angle) = 20 * tan(45) = 20 * 1 = 20 m.

A person is standing 20 m away from a building and sees the top of the building

Practice Questions

Q1
A person is standing 20 m away from a building and sees the top of the building at an angle of elevation of 45 degrees. What is the height of the building? (2019)
  1. 10 m
  2. 20 m
  3. 30 m
  4. 40 m

Questions & Step-by-Step Solutions

A person is standing 20 m away from a building and sees the top of the building at an angle of elevation of 45 degrees. What is the height of the building? (2019)
  • Step 1: Understand the problem. A person is standing 20 meters away from a building and sees the top of the building at an angle of elevation of 45 degrees.
  • Step 2: Identify the relevant information. The distance from the person to the building is 20 meters, and the angle of elevation is 45 degrees.
  • Step 3: Recall the formula to find the height of the building. The height can be calculated using the formula: Height = distance * tan(angle).
  • Step 4: Substitute the known values into the formula. Here, distance = 20 m and angle = 45 degrees.
  • Step 5: Calculate tan(45 degrees). The value of tan(45 degrees) is 1.
  • Step 6: Multiply the distance by the value of tan(45 degrees). So, Height = 20 m * 1.
  • Step 7: Calculate the final height. Therefore, Height = 20 m.
  • Trigonometry – The problem involves using the tangent function to relate the height of the building to the distance from the building and the angle of elevation.
  • Angle of Elevation – Understanding how the angle of elevation from a point to the top of an object can be used to calculate height.
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