Question

A boy is standing on the ground and flying a kite with 100m of sting at an elevation of 30°. Another boy is standing on the roof of a 10m high building and is flying his kite at an elevation of 45°. Both the boys are on opposite sides of both the kites. Find the length of the string that the second boy must have so that the two kites meet. 

Answer 1

Let C be the position of the first boy and D be the position of the second boy who is standing on the roof of a 10 m high building. 
Let B be the position of the kites of both the boys. 
Let AB = h and CA = x. 
In ΔABC, 
sin30° = `"h"/100`

⇒ `1/2 = "h"/100`

⇒ h = 50  ... (1)

In ΔBDE,

`tan45^circ = "BE"/"BD"`

⇒ `1 = ("h" - 10)/"X"`

⇒ X = (h - 10)  ...(2)

From (1) and (2), 
x = 50 - 10 = 40 

In ΔBDE,

`sin45^circ = "BE"/"BD"`

⇒ `1/sqrt(2) = ("h" - 10)/("BC")`

⇒ `"BC" = sqrt(2)(50-10) = 40sqrt(2)`

Thus, the required length of the string that the second boy must have `40sqrt(2)` m