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A kite is flying at a height of 40 meters. If the angle of elevation from a poin

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Question: A kite is flying at a height of 40 meters. If the angle of elevation from a point on the ground to the kite is 60 degrees, how far is the point from the base of the kite?

Options:

  1. 20√3 meters
  2. 40 meters
  3. 30 meters
  4. 50 meters

Correct Answer: 20√3 meters

Solution: 

Using tan(60) = 40/distance, distance = 40/tan(60) = 40/√3 = 20√3 meters.

A kite is flying at a height of 40 meters. If the angle of elevation from a poin

Practice Questions

Q1
A kite is flying at a height of 40 meters. If the angle of elevation from a point on the ground to the kite is 60 degrees, how far is the point from the base of the kite?
  1. 20√3 meters
  2. 40 meters
  3. 30 meters
  4. 50 meters

Questions & Step-by-Step Solutions

A kite is flying at a height of 40 meters. If the angle of elevation from a point on the ground to the kite is 60 degrees, how far is the point from the base of the kite?
  • Step 1: Understand that the height of the kite is 40 meters.
  • Step 2: Recognize that the angle of elevation from the ground to the kite is 60 degrees.
  • Step 3: Visualize a right triangle where the height of the kite is the opposite side (40 meters) and the distance from the point on the ground to the base of the kite is the adjacent side.
  • Step 4: Use the tangent function, which relates the opposite side to the adjacent side in a right triangle: tan(angle) = opposite/adjacent.
  • Step 5: Write the equation using the given values: tan(60 degrees) = 40/distance.
  • Step 6: Rearrange the equation to find the distance: distance = 40/tan(60 degrees).
  • Step 7: Calculate tan(60 degrees), which is √3.
  • Step 8: Substitute tan(60 degrees) into the equation: distance = 40/√3.
  • Step 9: Simplify the distance: distance = 40/√3 = 40 * (√3/3) = 20√3 meters.
  • Trigonometry – The problem involves using trigonometric ratios, specifically the tangent function, to relate the height of the kite and the distance from the point on the ground.
  • Angle of Elevation – Understanding the concept of angle of elevation is crucial for visualizing the scenario and applying the correct trigonometric function.
  • Right Triangle Properties – The scenario can be modeled as a right triangle, where the height of the kite is the opposite side and the distance from the point to the base of the kite is the adjacent side.
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