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A person is standing 40 meters away from a building and sees the top of the buil

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Question: A person is standing 40 meters 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?

Options:

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

Correct Answer: 40 meters

Solution: 

Using tan(45) = height/40, height = 40 * tan(45) = 40 meters.

A person is standing 40 meters away from a building and sees the top of the buil

Practice Questions

Q1
A person is standing 40 meters 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?
  1. 40 meters
  2. 30 meters
  3. 20 meters
  4. 50 meters

Questions & Step-by-Step Solutions

A person is standing 40 meters 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?
  • Step 1: Understand that the person is standing 40 meters away from the building.
  • Step 2: Know that the angle of elevation to the top of the building is 45 degrees.
  • Step 3: Recall that 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 building).
  • Step 4: Write the formula: tan(angle) = height / distance.
  • Step 5: Substitute the values into the formula: tan(45 degrees) = height / 40 meters.
  • Step 6: Know that tan(45 degrees) equals 1.
  • Step 7: Set up the equation: 1 = height / 40.
  • Step 8: Multiply both sides by 40 to solve for height: height = 40 * 1.
  • Step 9: Calculate the height: height = 40 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 the building.
  • Angle of Elevation – Understanding how the angle of elevation relates to the height and distance in a right triangle.
  • Right Triangle Properties – Applying properties of right triangles to solve for unknown lengths using trigonometric ratios.
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