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)

Answer 1

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.