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From a point on the ground, the angle of elevation to the top of a tree is 45 de

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Question: From a point on the ground, the angle of elevation to the top of a tree is 45 degrees. If the point is 20 meters away from the base of the tree, what is the height of the tree?

Options:

  1. 20 meters
  2. 10 meters
  3. 30 meters
  4. 15 meters

Correct Answer: 20 meters

Solution: 

Height = distance * tan(angle) = 20 * 1 = 20 meters.

From a point on the ground, the angle of elevation to the top of a tree is 45 de

Practice Questions

Q1
From a point on the ground, the angle of elevation to the top of a tree is 45 degrees. If the point is 20 meters away from the base of the tree, what is the height of the tree?
  1. 20 meters
  2. 10 meters
  3. 30 meters
  4. 15 meters

Questions & Step-by-Step Solutions

From a point on the ground, the angle of elevation to the top of a tree is 45 degrees. If the point is 20 meters away from the base of the tree, what is the height of the tree?
Correct Answer: 20 meters
  • Step 1: Understand the problem. You have a tree and a point on the ground that is 20 meters away from the base of the tree.
  • Step 2: Know that the angle of elevation to the top of the tree is 45 degrees. This means if you draw a line from the point on the ground to the top of the tree, it makes a 45-degree angle with the ground.
  • Step 3: Remember that when the angle of elevation is 45 degrees, the height of the tree is equal to the distance from the point to the base of the tree.
  • Step 4: Use the formula for height: Height = distance * tan(angle). Here, the distance is 20 meters and the angle is 45 degrees.
  • Step 5: Calculate tan(45 degrees). The value of tan(45 degrees) is 1.
  • Step 6: Substitute the values into the formula: Height = 20 meters * 1.
  • Step 7: Calculate the height: Height = 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 tree.
  • 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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