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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\'s height?

Options:

  1. 20√3 meters
  2. 40 meters
  3. 30 meters
  4. 10√3 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's height?
  1. 20√3 meters
  2. 40 meters
  3. 30 meters
  4. 10√3 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's height?
  • Step 1: Understand the problem. We have a kite flying at a height of 40 meters and we need to find the distance from a point on the ground to the base of the kite's height.
  • Step 2: Identify the angle of elevation. The angle from the ground to the kite is 60 degrees.
  • Step 3: Use the tangent function. The tangent of an angle in a right triangle is the opposite side (height of the kite) divided by the adjacent side (distance from the point to the base of the kite).
  • Step 4: Write the equation using the tangent function: tan(60 degrees) = height / distance.
  • Step 5: Substitute the known values into the equation: tan(60) = 40 / distance.
  • Step 6: Rearrange the equation to solve for distance: distance = 40 / tan(60).
  • Step 7: Calculate tan(60). The value of tan(60) is √3.
  • Step 8: Substitute tan(60) into the equation: distance = 40 / √3.
  • Step 9: Simplify the equation: distance = 40 / √3 = 40 * (√3 / 3) = 20√3 meters.
  • Step 10: Conclude that the distance from the point on the ground to the base of the kite's height is 20√3 meters.
  • Trigonometry – The problem involves using the tangent function to relate the height of the kite and the distance from the point on the ground.
  • Angle of Elevation – Understanding the angle of elevation is crucial for setting up the right triangle in the problem.
  • 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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