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A kite is flying at a height of 50 m. If the angle of elevation from a point on

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Question: A kite is flying at a height of 50 m. 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? (2021)

Options:

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

Correct Answer: 25 m

Exam Year: 2021

Solution: 

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

A kite is flying at a height of 50 m. If the angle of elevation from a point on

Practice Questions

Q1
A kite is flying at a height of 50 m. 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? (2021)
  1. 25 m
  2. 50 m
  3. 75 m
  4. 100 m

Questions & Step-by-Step Solutions

A kite is flying at a height of 50 m. 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? (2021)
  • Step 1: Understand that the kite is flying at a height of 50 meters above the ground.
  • Step 2: Recognize that the angle of elevation from the point on the ground to the kite is 60 degrees.
  • Step 3: Recall that the tangent of an angle in a right triangle is the ratio of the opposite side (height of the kite) to the adjacent side (distance from the point to the base of the kite).
  • Step 4: Set up the equation using the tangent function: tan(60 degrees) = height / distance.
  • Step 5: Substitute the known values into the equation: tan(60) = 50 / distance.
  • Step 6: Rearrange the equation to solve for distance: distance = height / tan(60).
  • Step 7: Calculate tan(60 degrees), which is √3.
  • Step 8: Substitute tan(60) into the equation: distance = 50 / √3.
  • Step 9: Simplify the calculation to find the distance: distance ≈ 25 meters.
  • Trigonometry – The problem involves using trigonometric functions to relate angles and distances in a right triangle.
  • Angle of Elevation – Understanding the concept of angle of elevation is crucial for visualizing the scenario and applying the correct trigonometric function.
  • Tangent Function – The tangent function relates the opposite side (height of the kite) to the adjacent side (distance from the base) in a right triangle.
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