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Question
A boy standing at a point O finds his kite flying at a point P with distance OP = 25 m. It is at a height of 5 m from the ground. When the thread is extended by 10 m from P, it reaches a point Q. What will be the height QN of the kite from the ground? (use trigonometric ratios)
Solution
Let the angle O be “θ”
In ΔONQ
sin θ = `"opposite side"/"hypotenuse" = "QN"/"OQ"`
sin θ = `"h"/((25 + 10))`
= `"h"/35` ...(1)
In ΔOMP
sin θ = `"PM"/"OP"`
⇒ sin θ = `5/25`
sin θ = `1/5` ...(2)
From (1) and (2) we get
`"h"/35 = 1/5`
5h = 35
⇒ h = `35/5`
= 7
The height of the kite from the ground is 7m.
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