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A drone is flying at a height of 50 meters. If the angle of depression from the

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Question: A drone is flying at a height of 50 meters. If the angle of depression from the drone to a point on the ground is 60 degrees, how far is the point from the base of the drone\'s vertical line?

Options:

  1. 25 meters
  2. 50 meters
  3. 75 meters
  4. 100 meters

Correct Answer: 25 meters

Solution: 

Distance = height/tan(60) = 50/(√3) = 50/√3 ≈ 25 meters.

A drone is flying at a height of 50 meters. If the angle of depression from the

Practice Questions

Q1
A drone is flying at a height of 50 meters. If the angle of depression from the drone to a point on the ground is 60 degrees, how far is the point from the base of the drone's vertical line?
  1. 25 meters
  2. 50 meters
  3. 75 meters
  4. 100 meters

Questions & Step-by-Step Solutions

A drone is flying at a height of 50 meters. If the angle of depression from the drone to a point on the ground is 60 degrees, how far is the point from the base of the drone's vertical line?
  • Step 1: Understand that the drone is flying at a height of 50 meters above the ground.
  • Step 2: Recognize that the angle of depression from the drone to the point on the ground is 60 degrees.
  • Step 3: Visualize a right triangle where the height of the drone is one side (50 meters) and the distance from the base of the drone's vertical line to the point on the ground is the other side.
  • Step 4: Use the tangent function, which relates the angle to the opposite side (height) and the adjacent side (distance). The formula is: tan(angle) = opposite/adjacent.
  • Step 5: Rearrange the formula to find the distance: distance = height / tan(angle).
  • Step 6: Substitute the values into the formula: distance = 50 / tan(60 degrees).
  • Step 7: Calculate tan(60 degrees), which is √3.
  • Step 8: Now substitute tan(60) with √3: distance = 50 / √3.
  • Step 9: To simplify, you can leave it as 50/√3 or calculate it to get approximately 25 meters.
  • Trigonometry – The problem involves using the tangent function to relate the height of the drone and the angle of depression to find the horizontal distance.
  • Angle of Depression – Understanding the angle of depression from the drone to the ground point is crucial for setting up the right triangle.
  • Right Triangle Properties – The relationship between the sides of a right triangle and the angles is fundamental to solving the problem.
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