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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 tree is 10 meters tall, how far is the point from the base of the tree?

Options:

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

Correct Answer: 10 meters

Solution: 

Distance = height / tan(angle) = 10 / 1 = 10 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 tree is 10 meters tall, how far is the point from the base of the tree?
  1. 10 meters
  2. 5 meters
  3. 15 meters
  4. 20 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 tree is 10 meters tall, how far is the point from the base of the tree?
Correct Answer: 10 meters
  • Step 1: Understand the problem. We have a tree that is 10 meters tall.
  • Step 2: The angle of elevation from the point on the ground to the top of the tree is 45 degrees.
  • Step 3: Recall that the tangent of an angle in a right triangle is the opposite side (height of the tree) divided by the adjacent side (distance from the point to the base of the tree).
  • Step 4: Write the formula for distance: Distance = height / tan(angle).
  • Step 5: Plug in the values: height = 10 meters and angle = 45 degrees.
  • Step 6: Calculate tan(45 degrees). The value of tan(45 degrees) is 1.
  • Step 7: Substitute the values into the formula: Distance = 10 meters / 1.
  • Step 8: Perform the calculation: Distance = 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 point to the base of the tree.
  • Right Triangle Properties – Understanding the properties of right triangles, specifically that at a 45-degree angle, the opposite and adjacent sides are equal.
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