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

Options:

  1. 50 meters
  2. 25 meters
  3. 35 meters
  4. 70 meters

Correct Answer: 50 meters

Solution: 

Using the tangent function, tan(45) = 50 / distance. Therefore, distance = 50 / tan(45) = 50 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 45 degrees, how far is the point from the base of the kite?
  1. 50 meters
  2. 25 meters
  3. 35 meters
  4. 70 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 45 degrees, how far is the point from the base of the kite?
  • Step 1: Understand that the kite is flying at a height of 50 meters above the ground.
  • Step 2: Know that the angle of elevation from the point on the ground to the kite is 45 degrees.
  • Step 3: Recall the tangent function in trigonometry, which relates the angle to the opposite side (height of the kite) and 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(45 degrees) = 50 meters / distance.
  • Step 6: Calculate tan(45 degrees), which equals 1.
  • Step 7: Set up the equation: 1 = 50 / distance.
  • Step 8: Rearrange the equation to find the distance: distance = 50 / 1.
  • Step 9: Calculate the distance, which equals 50 meters.
  • Trigonometry – The problem involves using the tangent function to relate the height of the kite and 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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