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From a point on the ground, the angle of elevation to the top of a hill is 30 de

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Question: From a point on the ground, the angle of elevation to the top of a hill is 30 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√3 meters
  2. 20 meters
  3. 30 meters
  4. 40 meters

Correct Answer: 10√3 meters

Solution: 

Height = distance * tan(30) = 20 * (1/√3) = 20/√3 = 10√3 meters.

From a point on the ground, the angle of elevation to the top of a hill is 30 de

Practice Questions

Q1
From a point on the ground, the angle of elevation to the top of a hill is 30 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√3 meters
  2. 20 meters
  3. 30 meters
  4. 40 meters

Questions & Step-by-Step Solutions

From a point on the ground, the angle of elevation to the top of a hill is 30 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 the problem. We need to find the height of the hill using the angle of elevation and the distance from the point to the base of the hill.
  • Step 2: Identify the given information. The angle of elevation is 30 degrees, and the distance from the point to the base of the hill is 20 meters.
  • Step 3: Recall the relationship between the angle of elevation, height, and distance. We can use the tangent function: tan(angle) = height / distance.
  • Step 4: Write the formula using the given angle. For 30 degrees, we have: tan(30 degrees) = height / 20 meters.
  • Step 5: Find the value of tan(30 degrees). It is equal to 1/√3.
  • Step 6: Substitute the value of tan(30 degrees) into the formula: 1/√3 = height / 20.
  • Step 7: Rearrange the formula to solve for height: height = 20 * (1/√3).
  • Step 8: Calculate the height: height = 20/√3.
  • Step 9: Simplify the height: height = 20/√3 = 10√3 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 point to the base.
  • Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the hill, the distance to the base, and the angle of elevation.
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