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A kite is flying at a height of 30 meters. If the angle of elevation from a poin

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Question: A kite is flying at a height of 30 meters. If the angle of elevation from a point on the ground to the kite is 45 degrees, how far is the point from the base of the kite?

Options:

  1. 15 m
  2. 30 m
  3. 45 m
  4. 60 m

Correct Answer: 30 m

Solution: 

Using tan(45°) = height/distance, we have 1 = 30/distance. Therefore, distance = 30 m.

A kite is flying at a height of 30 meters. If the angle of elevation from a poin

Practice Questions

Q1
A kite is flying at a height of 30 meters. If the angle of elevation from a point on the ground to the kite is 45 degrees, how far is the point from the base of the kite?
  1. 15 m
  2. 30 m
  3. 45 m
  4. 60 m

Questions & Step-by-Step Solutions

A kite is flying at a height of 30 meters. If the angle of elevation from a point on the ground to the kite is 45 degrees, how far is the point from the base of the kite?
  • Step 1: Understand that the height of the kite is 30 meters.
  • Step 2: Know that the angle of elevation from the ground to the kite is 45 degrees.
  • Step 3: Recall the tangent function in a right triangle: tan(angle) = opposite/adjacent.
  • Step 4: In this case, the opposite side is the height of the kite (30 meters) and the adjacent side is the distance from the point on the ground to the base of the kite.
  • Step 5: Set up the equation using the tangent of 45 degrees: tan(45°) = height/distance.
  • Step 6: Since tan(45°) equals 1, we can write the equation as 1 = 30/distance.
  • Step 7: Rearrange the equation to find the distance: distance = 30 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 scenario and applying trigonometric functions correctly.
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