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A kite is flying at a height of 50 meters. If the angle of elevation from a poin

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Question: A kite is flying at a height of 50 meters. If the angle of elevation from a point on the ground is 30 degrees, how far is the point from the base of the kite?

Options:

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

Correct Answer: 50√3

Solution: 

distance = height / tan(30) = 50 / (1/√3) = 50√3 meters

A kite is flying at a height of 50 meters. If the angle of elevation from a poin

Practice Questions

Q1
A kite is flying at a height of 50 meters. If the angle of elevation from a point on the ground is 30 degrees, how far is the point from the base of the kite?
  1. 50√3
  2. 25√3
  3. 75√3
  4. 100√3

Questions & Step-by-Step Solutions

A kite is flying at a height of 50 meters. If the angle of elevation from a point on the ground is 30 degrees, how far is the point from the base of the kite?
Correct Answer: 50√3 meters
  • Step 1: Understand that the height of the kite is 50 meters.
  • Step 2: Know that the angle of elevation from the point on the ground to the kite is 30 degrees.
  • Step 3: Recall that 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 formula for tangent: tan(angle) = opposite / adjacent.
  • Step 5: Substitute the known values into the formula: tan(30 degrees) = height / distance.
  • Step 6: Rearrange the formula to find distance: distance = height / tan(30 degrees).
  • Step 7: Calculate tan(30 degrees), which is 1/√3.
  • Step 8: Substitute the height (50 meters) and tan(30 degrees) into the formula: distance = 50 / (1/√3).
  • Step 9: Simplify the calculation: distance = 50 * √3.
  • Step 10: Conclude that the distance from the point to the base of the kite is 50√3 meters.
  • Trigonometry – The problem involves using the tangent function to relate the height of the kite to 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 this scenario.
  • Right Triangle Properties – The relationship between the sides of a right triangle is key to solving for the distance.
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