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A tree is 15 meters tall. If the angle of elevation from a point on the ground t

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Question: A tree is 15 meters tall. If the angle of elevation from a point on the ground to the top of the tree is 30 degrees, how far is the point from the base of the tree?

Options:

  1. 15√3 meters
  2. 15/√3 meters
  3. 15 meters
  4. 30 meters

Correct Answer: 15/√3 meters

Solution: 

Using tan(30) = height/distance, distance = height/tan(30) = 15/√3 meters.

A tree is 15 meters tall. If the angle of elevation from a point on the ground t

Practice Questions

Q1
A tree is 15 meters tall. If the angle of elevation from a point on the ground to the top of the tree is 30 degrees, how far is the point from the base of the tree?
  1. 15√3 meters
  2. 15/√3 meters
  3. 15 meters
  4. 30 meters

Questions & Step-by-Step Solutions

A tree is 15 meters tall. If the angle of elevation from a point on the ground to the top of the tree is 30 degrees, how far is the point from the base of the tree?
  • Step 1: Understand the problem. We have a tree that is 15 meters tall and we want to find out how far away a point on the ground is from the base of the tree.
  • Step 2: Identify the angle of elevation. The angle from the point on the ground to the top of the tree is 30 degrees.
  • Step 3: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the tree) divided by the adjacent side (distance from the tree).
  • Step 4: Write the formula. We can write this as tan(30 degrees) = height / distance.
  • Step 5: Plug in the height of the tree. We know the height is 15 meters, so we have tan(30 degrees) = 15 / distance.
  • Step 6: Rearrange the formula to find distance. We can rearrange it to distance = height / tan(30 degrees).
  • Step 7: Calculate tan(30 degrees). The value of tan(30 degrees) is √3 / 3.
  • Step 8: Substitute tan(30 degrees) into the formula. Now we have distance = 15 / (√3 / 3).
  • Step 9: Simplify the equation. This simplifies to distance = 15 * (3 / √3).
  • Step 10: Calculate the final distance. This gives us distance = 15 * (3 / √3) = 15√3 meters.
  • Trigonometry – The problem involves using the tangent function to relate the height of the tree to the distance from the base using the angle of elevation.
  • 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 angle of elevation.
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