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A kite is flying at a height of 50 m. If the angle of elevation from a point on

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Question: A kite is flying at a height of 50 m. 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? (2020)

Options:

  1. 50 m
  2. 70 m
  3. 100 m
  4. 30 m

Correct Answer: 50 m

Exam Year: 2020

Solution: 

Using tan(45) = 1, distance = height = 50 m.

A kite is flying at a height of 50 m. If the angle of elevation from a point on

Practice Questions

Q1
A kite is flying at a height of 50 m. 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? (2020)
  1. 50 m
  2. 70 m
  3. 100 m
  4. 30 m

Questions & Step-by-Step Solutions

A kite is flying at a height of 50 m. 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? (2020)
  • 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 45 degrees.
  • Step 3: Recall that the tangent of an angle in a right triangle is the ratio of the opposite side (height) to the adjacent side (distance from the point to the base of the kite).
  • Step 4: Use the formula: tan(angle) = opposite/adjacent.
  • Step 5: Substitute the values: tan(45 degrees) = height/distance.
  • Step 6: Since tan(45 degrees) equals 1, we have 1 = 50/distance.
  • Step 7: Rearrange the equation to find distance: distance = height.
  • Step 8: Therefore, the distance from the point on the ground to the base of the kite is 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 principles.
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