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From a point 60 meters away from the base of a hill, the angle of elevation to t

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Question: From a point 60 meters away from the base of a hill, the angle of elevation to the top of the hill is 30 degrees. What is the height of the hill?

Options:

  1. 20 meters
  2. 30 meters
  3. 40 meters
  4. 50 meters

Correct Answer: 30 meters

Solution: 

Height = distance * tan(angle) = 60 * (1/√3) = 60 / 1.732 = 34.64 meters.

From a point 60 meters away from the base of a hill, the angle of elevation to t

Practice Questions

Q1
From a point 60 meters away from the base of a hill, the angle of elevation to the top of the hill is 30 degrees. What is the height of the hill?
  1. 20 meters
  2. 30 meters
  3. 40 meters
  4. 50 meters

Questions & Step-by-Step Solutions

From a point 60 meters away from the base of a hill, the angle of elevation to the top of the hill is 30 degrees. What is the height of the hill?
Correct Answer: 34.64 meters
  • Step 1: Understand the problem. You are looking for the height of a hill from a point 60 meters away.
  • Step 2: Identify the angle of elevation. The angle given is 30 degrees.
  • Step 3: Recall the relationship between the height of the hill, the distance from the hill, and the angle of elevation. This can be calculated using the tangent function: tan(angle) = height / distance.
  • Step 4: Rearrange the formula to find the height: height = distance * tan(angle).
  • Step 5: Substitute the values into the formula. Here, distance = 60 meters and angle = 30 degrees.
  • Step 6: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3 or approximately 0.577.
  • Step 7: Multiply the distance by the tangent value: height = 60 * (1/√3).
  • Step 8: Calculate the height: height = 60 / 1.732, which is approximately 34.64 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.
  • Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the hill, the distance from the base, and the angle of elevation.
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