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From a point on the ground, the angle of elevation to the top of a building is 4

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Question: From a point on the ground, the angle of elevation to the top of a building is 45 degrees. If the building is 50 meters tall, how far is the point from the base of the building?

Options:

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

Correct Answer: 50 m

Solution: 

Distance = height / tan(angle) = 50 / 1 = 50 m.

From a point on the ground, the angle of elevation to the top of a building is 4

Practice Questions

Q1
From a point on the ground, the angle of elevation to the top of a building is 45 degrees. If the building is 50 meters tall, how far is the point from the base of the building?
  1. 50 m
  2. 25 m
  3. 100 m
  4. 75 m

Questions & Step-by-Step Solutions

From a point on the ground, the angle of elevation to the top of a building is 45 degrees. If the building is 50 meters tall, how far is the point from the base of the building?
  • Step 1: Understand that the angle of elevation is the angle formed between the horizontal line from your point on the ground and the line of sight to the top of the building.
  • Step 2: Recognize that the height of the building is 50 meters.
  • Step 3: Note that the angle of elevation is 45 degrees.
  • Step 4: 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 point to the base of the building).
  • Step 5: For a 45-degree angle, the tangent value is 1 (tan(45 degrees) = 1).
  • Step 6: Use the formula: Distance = height / tan(angle).
  • Step 7: Substitute the values into the formula: Distance = 50 meters / 1.
  • Step 8: Calculate the distance: Distance = 50 meters.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height and distance from the building.
  • Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the building, the distance from the point to the base, and the angle of elevation.
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