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

Options:

  1. 10 meters
  2. 5 meters
  3. 15 meters
  4. 20 meters

Correct Answer: 10 meters

Solution: 

Let h be the height of the hill. tan(45°) = h/10. Therefore, h = 10 * tan(45°) = 10 * 1 = 10 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 10 meters away from the base of the hill, what is the height of the hill?
  1. 10 meters
  2. 5 meters
  3. 15 meters
  4. 20 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 10 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 ground and the line of sight to the top of the hill.
  • Step 2: Identify that the angle of elevation is 45 degrees.
  • Step 3: Recognize that the distance from the point on the ground to the base of the hill is 10 meters.
  • 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) = opposite/adjacent.
  • Step 5: In this case, the opposite side is the height of the hill (h) and the adjacent side is the distance from the point to the base of the hill (10 meters). So, tan(45°) = h/10.
  • Step 6: Since tan(45°) equals 1, we can write the equation as 1 = h/10.
  • Step 7: To find h, multiply both sides of the equation by 10: h = 10 * 1.
  • Step 8: Calculate h, which gives us h = 10 meters.
  • Trigonometry – The problem tests the understanding of the tangent function in right triangles, specifically how to relate angles and side lengths.
  • Angle of Elevation – The question involves interpreting the angle of elevation from a point on the ground to the top of a hill.
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