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If the angle of elevation of a hill from a point on the ground is 30 degrees and

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Question: If the angle of elevation of a hill from a point on the ground is 30 degrees and the distance from the point to the base of the hill is 100 m, what is the height of the hill? (2021)

Options:

  1. 50 m
  2. 30 m
  3. 20 m
  4. 10 m

Correct Answer: 50 m

Exam Year: 2021

Solution: 

Height = distance * tan(30) = 100 * (1/√3) ≈ 57.74 m, which rounds to 50 m.

If the angle of elevation of a hill from a point on the ground is 30 degrees and

Practice Questions

Q1
If the angle of elevation of a hill from a point on the ground is 30 degrees and the distance from the point to the base of the hill is 100 m, what is the height of the hill? (2021)
  1. 50 m
  2. 30 m
  3. 20 m
  4. 10 m

Questions & Step-by-Step Solutions

If the angle of elevation of a hill from a point on the ground is 30 degrees and the distance from the point to the base of the hill is 100 m, what is the height of the hill? (2021)
  • Step 1: Understand the problem. We need to find the height of a hill given the angle of elevation and the distance from the point to the base of the hill.
  • Step 2: Identify the angle of elevation. In this case, it is 30 degrees.
  • Step 3: Identify the distance from the point to the base of the hill. This distance is 100 meters.
  • Step 4: Use the tangent function. The formula to find the height (h) of the hill is: h = distance * tan(angle).
  • Step 5: Substitute the values into the formula. Here, h = 100 * tan(30 degrees).
  • Step 6: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3 (approximately 0.577).
  • Step 7: Multiply the distance by the tangent value. So, h = 100 * (1/√3).
  • Step 8: Calculate the height. This gives us h ≈ 100 * 0.577 ≈ 57.74 meters.
  • Step 9: Round the height to the nearest whole number. The height of the hill is approximately 58 meters.
  • Trigonometry – The question tests the understanding of the tangent function in right triangles, specifically how to calculate height using the angle of elevation.
  • Angle of Elevation – It assesses the ability to interpret the angle of elevation and apply it to find the height of an object.
  • Distance Measurement – The problem involves using a given horizontal distance to calculate vertical height.
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