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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 height of the hill is 100 m, how far is the point from the base of the hill? (2022)

Options:

  1. 173.21 m
  2. 100 m
  3. 200 m
  4. 150 m

Correct Answer: 173.21 m

Exam Year: 2022

Solution: 

Distance = height / tan(30) = 100 / (1/√3) = 100√3 ≈ 173.21 m.

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 height of the hill is 100 m, how far is the point from the base of the hill? (2022)
  1. 173.21 m
  2. 100 m
  3. 200 m
  4. 150 m

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 height of the hill is 100 m, how far is the point from the base of the hill? (2022)
  • Step 1: Understand the problem. We have a hill that is 100 meters tall, and we want to find out how far away we are from the base of the hill when looking up at it at a 30-degree angle.
  • Step 2: Recall the relationship between the height of the hill, the distance from the base, and the angle of elevation. We can use the tangent function, which is defined as the opposite side (height of the hill) over the adjacent side (distance from the base).
  • Step 3: Write the formula for tangent: tan(angle) = opposite / adjacent. In our case, tan(30 degrees) = height / distance.
  • Step 4: Plug in the values we know. We have height = 100 m and angle = 30 degrees. So, tan(30 degrees) = 100 / distance.
  • Step 5: Find the value of tan(30 degrees). It is equal to 1/√3.
  • Step 6: Set up the equation: 1/√3 = 100 / distance.
  • Step 7: Rearrange the equation to solve for distance: distance = 100 / (1/√3).
  • Step 8: Simplify the equation: distance = 100 * √3.
  • Step 9: Calculate the distance: distance ≈ 173.21 m.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height and distance from the base of the hill.
  • Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the hill and the distance from the point on the ground.
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