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From a point on the ground, the angle of elevation to the top of a hill is 45 de

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Question: From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the distance from the point to the base of the hill is 20 meters, what is the height of the hill?

Options:

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

Correct Answer: 20 m

Solution: 

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

From a point on the ground, the angle of elevation to the top of a hill is 45 de

Practice Questions

Q1
From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the distance from the point to the base of the hill is 20 meters, what is the height of the hill?
  1. 10 m
  2. 20 m
  3. 30 m
  4. 40 m

Questions & Step-by-Step Solutions

From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the distance from the point to the base of the hill is 20 meters, what is the height of the hill?
  • 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 hill.
  • Step 2: Note that the angle of elevation is given as 45 degrees.
  • Step 3: Recognize that the distance from your point to the base of the hill is 20 meters.
  • Step 4: Use the tangent function, which relates the angle of elevation to the height of the hill and the distance to the base. The formula is: height = distance * tan(angle).
  • Step 5: Since the angle is 45 degrees, we know that tan(45 degrees) equals 1.
  • Step 6: Substitute the values into the formula: height = 20 meters * tan(45 degrees).
  • Step 7: Calculate the height: height = 20 meters * 1 = 20 meters.
  • Step 8: Conclude that the height of the hill is 20 meters.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height and distance from the base of the hill.
  • Angle of Elevation – Understanding how the angle of elevation relates to the height of an object and the horizontal distance from the observer.
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