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A person is standing 30 m away from a tree and observes the top of the tree at a

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Question: A person is standing 30 m away from a tree and observes the top of the tree at an angle of elevation of 60 degrees. What is the height of the tree? (2022)

Options:

  1. 15 m
  2. 20 m
  3. 25 m
  4. 30 m

Correct Answer: 25 m

Exam Year: 2022

Solution: 

Height = distance * tan(angle) = 30 * tan(60) = 30 * √3 ≈ 25 m.

A person is standing 30 m away from a tree and observes the top of the tree at a

Practice Questions

Q1
A person is standing 30 m away from a tree and observes the top of the tree at an angle of elevation of 60 degrees. What is the height of the tree? (2022)
  1. 15 m
  2. 20 m
  3. 25 m
  4. 30 m

Questions & Step-by-Step Solutions

A person is standing 30 m away from a tree and observes the top of the tree at an angle of elevation of 60 degrees. What is the height of the tree? (2022)
  • Step 1: Understand the situation. A person is standing 30 meters away from a tree and looking up at the top of the tree.
  • Step 2: Identify the angle of elevation. The angle at which the person looks up to see the top of the tree is 60 degrees.
  • Step 3: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the tree) divided by the adjacent side (distance from the tree).
  • Step 4: Set up the equation. We can write the equation as: height = distance * tan(angle). Here, distance is 30 meters and angle is 60 degrees.
  • Step 5: Calculate tan(60 degrees). The value of tan(60 degrees) is √3 (approximately 1.732).
  • Step 6: Substitute the values into the equation. Height = 30 * tan(60) = 30 * √3.
  • Step 7: Calculate the height. Height ≈ 30 * 1.732 ≈ 51.96 meters.
  • Step 8: Round the answer. The height of the tree is approximately 52 meters.
  • Trigonometry – The problem involves using the tangent function to relate the height of the tree to the distance from the observer and the angle of elevation.
  • Angle of Elevation – Understanding how the angle of elevation from the observer's line of sight to the top of the tree is used to calculate height.
  • Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the tree is the opposite side, the distance from the tree is the adjacent side, and the angle of elevation is the angle between them.
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