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A person is standing on the ground and looking at the top of a tree. If the angl

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Question: A person is standing on the ground and looking at the top of a tree. If the angle of elevation is 60 degrees and the person is 20 meters away from the tree, what is the height of the tree?

Options:

  1. 20√3 meters
  2. 10√3 meters
  3. 30 meters
  4. 40 meters

Correct Answer: 20√3 meters

Solution: 

Height = distance * tan(angle) = 20 * tan(60°) = 20 * √3 meters.

A person is standing on the ground and looking at the top of a tree. If the angl

Practice Questions

Q1
A person is standing on the ground and looking at the top of a tree. If the angle of elevation is 60 degrees and the person is 20 meters away from the tree, what is the height of the tree?
  1. 20√3 meters
  2. 10√3 meters
  3. 30 meters
  4. 40 meters

Questions & Step-by-Step Solutions

A person is standing on the ground and looking at the top of a tree. If the angle of elevation is 60 degrees and the person is 20 meters away from the tree, what is the height of the tree?
  • Step 1: Understand the problem. You have a person looking at the top of a tree from a distance of 20 meters.
  • Step 2: Identify the angle of elevation. The angle at which the person looks up to the top of the tree is 60 degrees.
  • Step 3: Recall the relationship between the height of the tree, the distance from the tree, and the angle of elevation. This can be calculated using the tangent function.
  • Step 4: Write down the formula for height: Height = distance * tan(angle).
  • Step 5: Substitute the known values into the formula: Height = 20 * tan(60 degrees).
  • Step 6: Calculate tan(60 degrees). The value of tan(60 degrees) is √3.
  • Step 7: Multiply the distance by the value of tan(60 degrees): Height = 20 * √3.
  • Step 8: The height of the tree is 20√3 meters.
  • Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the tree and the distance from the tree.
  • Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the tree, the distance from the tree, and the line of sight.
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