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A person looks at the top of a tree from a distance of 40 meters. If the angle o

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Question: A person looks at the top of a tree from a distance of 40 meters. If the angle of elevation is 30 degrees, what is the height of the tree?

Options:

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

Correct Answer: 20 meters

Solution: 

Height = distance * tan(angle) = 40 * (1/√3) ≈ 20 meters.

A person looks at the top of a tree from a distance of 40 meters. If the angle o

Practice Questions

Q1
A person looks at the top of a tree from a distance of 40 meters. If the angle of elevation is 30 degrees, what is the height of the tree?
  1. 20 meters
  2. 30 meters
  3. 40 meters
  4. 50 meters

Questions & Step-by-Step Solutions

A person looks at the top of a tree from a distance of 40 meters. If the angle of elevation is 30 degrees, what is the height of the tree?
Correct Answer: 20 meters
  • Step 1: Understand the problem. You need to find the height of a tree when you know the distance from the tree and the angle you are looking up at the top of the tree.
  • Step 2: Identify the distance from the person to the tree. In this case, it is 40 meters.
  • Step 3: Identify the angle of elevation. Here, it is 30 degrees.
  • Step 4: Use the tangent function. The formula to find the height (h) of the tree is: h = distance * tan(angle).
  • Step 5: Substitute the values into the formula. So, h = 40 * 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 = 40 * (1/√3).
  • Step 8: Calculate the height. This gives you approximately 20 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 observer.
  • Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the tree, the distance from the observer, and the angle of elevation.
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