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A kite is flying at the height of 75 m from the ground. The string makes an angle q (where cot θ = 8/15) with the level ground. Assuming that there is no slack in the string, the length of the string is equal to:    (SSC CGL 1st Sit. 2015)
  • a)
    75 m
  • b)
    85 m
  • c)
    40 m
  • d)
    65 m
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A kite is flying at the height of 75 m from the ground. The string mak...
Understanding the Problem
To find the length of the kite string, we need to consider the right triangle formed by the height of the kite, the horizontal distance from the point directly below the kite to the point on the ground where the string is anchored, and the string itself.
Given Information
- Height of the kite (opposite side) = 75 m
- cot(θ) = 8/15
Finding the Angle θ
Since cot(θ) = adjacent/opposite, we can interpret this as:
- Adjacent side = 8x
- Opposite side = 15x
Here, the opposite refers to the height of the kite, which is 75 m:
15x = 75
=> x = 5
Thus, the adjacent side (horizontal distance) is:
Adjacent = 8x = 8 * 5 = 40 m
Using Pythagorean Theorem
To find the length of the string (hypotenuse), we can apply the Pythagorean theorem:
Length of string = √(opposite² + adjacent²)
= √(75² + 40²)
= √(5625 + 1600)
= √7225
= 85 m
Conclusion
Thus, the length of the string is 85 m. The correct answer is option 'B'.
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A kite is flying at the height of 75 m from the ground. The string mak...

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