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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 point is 50 meters away from the base of the hill, what is the height of the hill?

Options:

  1. 50 meters
  2. 25 meters
  3. 70 meters
  4. 45 meters

Correct Answer: 50 meters

Solution: 

Using tan(45°) = height/50, height = 50 * tan(45°) = 50 meters.

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 point is 50 meters away from the base of the hill, what is the height of the hill?
  1. 50 meters
  2. 25 meters
  3. 70 meters
  4. 45 meters

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 point is 50 meters away from the base of the hill, what is the height of the hill?
  • Step 1: Understand that the angle of elevation is the angle formed between the horizontal line from the point on the ground and the line of sight to the top of the hill.
  • Step 2: Identify that the distance from the point on the ground to the base of the hill is 50 meters.
  • Step 3: Recognize that the angle of elevation to the top of the hill is 45 degrees.
  • Step 4: Use the tangent function, which relates the angle of elevation to the height of the hill and the distance from the base. The formula is: tan(angle) = height / distance.
  • Step 5: Substitute the known values into the formula: tan(45°) = height / 50.
  • Step 6: Know that tan(45°) equals 1. So, the equation becomes: 1 = height / 50.
  • Step 7: Solve for height by multiplying both sides of the equation by 50: height = 50 * 1.
  • Step 8: Calculate the height, which equals 50 meters.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the hill and the distance from the base.
  • 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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