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A kite is flying at a height of 60 meters. If the angle of elevation from a poin

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Question: A kite is flying at a height of 60 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. 60√3 meters
  2. 30√3 meters
  3. 20√3 meters
  4. 10√3 meters

Correct Answer: 60√3 meters

Solution: 

Distance = height / tan(angle) = 60 / (1/√3) = 60√3 meters.

A kite is flying at a height of 60 meters. If the angle of elevation from a poin

Practice Questions

Q1
A kite is flying at a height of 60 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. 60√3 meters
  2. 30√3 meters
  3. 20√3 meters
  4. 10√3 meters

Questions & Step-by-Step Solutions

A kite is flying at a height of 60 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?
Correct Answer: 60√3 meters
  • Step 1: Understand that the height of the kite is 60 meters.
  • Step 2: Know that the angle of elevation from 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 distance: Distance = height / tan(angle).
  • Step 5: Substitute the height (60 meters) and the angle (30 degrees) into the formula.
  • Step 6: Calculate tan(30 degrees), which is 1/√3.
  • Step 7: Now, plug this value into the formula: Distance = 60 / (1/√3).
  • Step 8: Simplify the equation: Distance = 60 * √3.
  • Step 9: The final answer is that the distance from the point to the base of the kite is 60√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 concept of angle of elevation is crucial for visualizing the problem and applying the correct trigonometric relationships.
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