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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 to the kite is 30 degrees, how far is the point from the base of the kite?

Options:

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

Correct Answer: 25√3 meters

Solution: 

Distance = height / tan(angle) = 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 to the kite is 30 degrees, how far is the point from the base of the kite?
  1. 50√3 meters
  2. 25√3 meters
  3. 100 meters
  4. 75 meters

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 to the kite is 30 degrees, how far is the point from the base of the kite?
  • Step 1: Understand that the height of the kite is 50 meters.
  • Step 2: Know that the angle of elevation from the ground to the kite is 30 degrees.
  • Step 3: Recognize that we can use the tangent function in a right triangle to find the distance from the point on the ground to the base of the kite.
  • Step 4: Recall the formula for tangent: tan(angle) = opposite / adjacent.
  • Step 5: In this case, the opposite side is the height of the kite (50 meters) and the adjacent side is the distance we want to find.
  • Step 6: Rearrange the formula to find the distance: distance = height / tan(angle).
  • Step 7: Substitute the values into the formula: distance = 50 / tan(30 degrees).
  • Step 8: Know that tan(30 degrees) is equal to 1/√3.
  • Step 9: Substitute tan(30 degrees) into the formula: distance = 50 / (1/√3).
  • Step 10: Simplify the equation: distance = 50 * √3.
  • Step 11: Therefore, the distance from the point on the ground 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 and the angle of elevation to find the horizontal distance.
  • Right Triangle Properties – Understanding the relationship between the sides of a right triangle formed by the height of the kite and the distance from the point on the ground.
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