Question

A boy standing at a point o finds his kites flying at a point p with distance op=25m .It is at a height of 5m from the ground.When the thread is extended by 10m from p, it reaches a point q.What will be the height qn of the kite from the ground?

Answer 1

Answer:

The height of the kite from the ground = 7 meters

Step-by-step explanation:

For better understanding of the solution see the figure attached :

The point p where the kite was flying initially make right angle with the ground surface ⇒ m∠OMP = 90°

Similarly, the point q where the kite was flying after extending the thread by 10 m also make right angle with the ground surface. ⇒ m∠ONQ = 90°

OQ = OP + PQ

⇒ OQ = 25 + 10 = 35 meters

Now, In ΔOMP and ΔONQ

∠O is common angle

m∠OMP = m∠ONQ = 90°

So, By AA postulate of similarity of triangles, ΔOMP ~ ΔONQ

Now, The sides of similar triangles are proportional to each other.

$\implies \frac{OP}{OQ}=\frac{PM}{QN}\\\\\implies \frac{25}{35}=\frac{5}{QN}\\\\\implies QN=\frac{35\times 5}{25}\\\\\bf\implies QN=7\thinspace{ meters}$

Hence, The height of the kite from the ground = 7 meters