A boy is standing on the ground and flying a kite with 100 m of string at an elevation of 30°. Another boy is standing on the roof of a 10 m 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.

Question

A boy is standing on the ground and flying a kite with 100 m of string at an elevation of 30&#xB0;. Another boy is standing on the roof of a 10 m high building and is flying his kite at an elevation of 45&#xB0;. 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.

Philoid · Accepted Answer

In the fig ‘C’ is the position of the kites. Let the length of second kite string is h.

In ∆ABC

Sin 30° =

=

20 + 2x = 100

x = 40m ………….(1)

In ∆CFD

Sin 45° =

=

h = √2 x …………….(2)

On substituting value

of x from eqn (1) in eqn (2)

h = √2 × 40 ⇒ 40√2 m

Therefore length of string of second kite is 40√2 m