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

Options:

  1. 100 meters
  2. 50 meters
  3. 200 meters
  4. 150 meters

Correct Answer: 100 meters

Solution: 

Height = distance * tan(angle) = 100 * tan(45°) = 100 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 100 meters away from the base of the hill, what is the height of the hill?
  1. 100 meters
  2. 50 meters
  3. 200 meters
  4. 150 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 100 meters away from the base of the hill, what is the height of the hill?
  • Step 1: Understand the problem. We have a point on the ground and a hill. We need to find the height of the hill.
  • Step 2: Identify the angle of elevation. The angle of elevation to the top of the hill is given as 45 degrees.
  • Step 3: Identify the distance from the point to the base of the hill. This distance is 100 meters.
  • Step 4: Recall the relationship between the height of the hill, the distance from the point to the base, and the angle of elevation. We can use the tangent function: tan(angle) = height / distance.
  • Step 5: Rearrange the formula to find the height: height = distance * tan(angle).
  • Step 6: Substitute the values into the formula: height = 100 meters * tan(45 degrees).
  • Step 7: Calculate tan(45 degrees). The value of tan(45 degrees) is 1.
  • Step 8: Multiply the distance by the tangent value: height = 100 meters * 1.
  • Step 9: Conclude that the height of the hill is 100 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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