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From a point on the ground, the angle of elevation to the top of a 75 m high bui

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Question: From a point on the ground, the angle of elevation to the top of a 75 m high building is 45 degrees. How far is the point from the building?

Options:

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

Correct Answer: 75 m

Solution: 

Using tan(45°) = height/distance, we have distance = height/tan(45°) = 75/1 = 75 m.

From a point on the ground, the angle of elevation to the top of a 75 m high bui

Practice Questions

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

Questions & Step-by-Step Solutions

From a point on the ground, the angle of elevation to the top of a 75 m high building is 45 degrees. How far is the point from the building?
  • Step 1: Understand that the angle of elevation is the angle formed between the horizontal ground and the line of sight to the top of the building.
  • Step 2: Identify the height of the building, which is given as 75 meters.
  • Step 3: Recognize that the angle of elevation to the top of the building is 45 degrees.
  • Step 4: Use the tangent function, which relates the angle of elevation to the height of the building and the distance from the building. The formula is: tan(angle) = height/distance.
  • Step 5: Substitute the known values into the formula: tan(45°) = height/distance, which becomes tan(45°) = 75/distance.
  • Step 6: Know that tan(45°) equals 1. So, the equation simplifies to: 1 = 75/distance.
  • Step 7: Rearrange the equation to find the distance: distance = 75/1.
  • Step 8: Calculate the distance, which equals 75 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 point to the building.
  • Angle of Elevation – Understanding the concept of angle of elevation is crucial for visualizing the problem and applying the correct trigonometric function.
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