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A person standing on the ground observes the top of a tree at an angle of elevat

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Question: A person standing on the ground observes the top of a tree at an angle of elevation of 45 degrees. If the person is 10 meters away from the tree, what is the height of the tree?

Options:

  1. 5 m
  2. 10 m
  3. 15 m
  4. 20 m

Correct Answer: 10 m

Solution: 

Using tan(45°) = height/10, we have 1 = height/10. Therefore, height = 10 m.

A person standing on the ground observes the top of a tree at an angle of elevat

Practice Questions

Q1
A person standing on the ground observes the top of a tree at an angle of elevation of 45 degrees. If the person is 10 meters away from the tree, what is the height of the tree?
  1. 5 m
  2. 10 m
  3. 15 m
  4. 20 m

Questions & Step-by-Step Solutions

A person standing on the ground observes the top of a tree at an angle of elevation of 45 degrees. If the person is 10 meters away from the tree, what is the height of the tree?
  • Step 1: Understand that the angle of elevation is the angle formed between the ground and the line of sight to the top of the tree.
  • Step 2: Note that the angle of elevation is 45 degrees.
  • Step 3: Recognize that the person is standing 10 meters away from the base of the tree.
  • Step 4: Use the tangent function, which relates the angle of elevation to the height of the tree and the distance from the tree.
  • Step 5: Write the formula: tan(angle) = height / distance.
  • Step 6: Substitute the known values into the formula: tan(45°) = height / 10.
  • Step 7: Know that tan(45°) equals 1.
  • Step 8: Set up the equation: 1 = height / 10.
  • Step 9: Solve for height by multiplying both sides by 10: height = 10 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.
  • Angle of Elevation – Understanding how the angle of elevation relates to the height of an object and the distance from the observer.
  • 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 given.
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