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A man is standing 100 meters away from a building. If the angle of elevation to

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Question: A man is standing 100 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?

Options:

  1. 100 m
  2. 50 m
  3. 75 m
  4. 25 m

Correct Answer: 100 m

Solution: 

Using tan(45°) = height/distance, we have height = distance * tan(45°) = 100 * 1 = 100 m.

A man is standing 100 meters away from a building. If the angle of elevation to

Practice Questions

Q1
A man is standing 100 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?
  1. 100 m
  2. 50 m
  3. 75 m
  4. 25 m

Questions & Step-by-Step Solutions

A man is standing 100 meters away from a building. If the angle of elevation to the top of the building is 45 degrees, what is the height of the building?
  • Step 1: Understand the problem. A man is standing 100 meters away from a building.
  • Step 2: Identify the angle of elevation to the top of the building, which is 45 degrees.
  • Step 3: Recall the tangent function in trigonometry: tan(angle) = opposite side / adjacent side.
  • Step 4: In this scenario, the 'opposite side' is the height of the building, and the 'adjacent side' is the distance from the man to the building (100 meters).
  • Step 5: Write the equation using the tangent function: tan(45°) = height / 100.
  • Step 6: Know that tan(45°) equals 1. So, the equation becomes: 1 = height / 100.
  • Step 7: To find the height, multiply both sides of the equation by 100: height = 100 * 1.
  • Step 8: Calculate the height: height = 100 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.
  • Angle of Elevation – Understanding how the angle of elevation relates to the height and distance in a right triangle.
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